Exhibit 5.1

Biohaven Limited

Kingston Chambers

PO Box 173

Road Town

Tortola, VG1110

British Virgin Islands

2 October 2023

Dear Sirs

Biohaven Limited (the “Company”)

We have acted as counsel as to British Virgin Islands law to the Company and have been asked to provide this legal opinion in connection with the Company’s registration statement on Form S-3ASR, including all amendments or supplements thereto, filed with the United States Securities and Exchange Commission (the “Commission”) under the United States Securities Act of 1933 (the “SECAct”), as amended (the “Registration Statement”), which allows for the registration of offerings and sales or resales of an indeterminate amount of one or more of the following categories of securities by the Company: (i) common shares, no par value (the “Common Shares”), (ii) preferred shares, no par value (the “Preferred Shares”, together with the Common Shares, the “Shares”), (iii) depositary shares or depositary receipts representing Preferred Shares (the “Depositary Shares”), (iv) debt securities (the “Debt Securities”), (v) warrants (the “Warrants”) to purchase Debt Securities, Common Shares or Preferred Shares, (vi) rights (the “Rights”) to purchase Securities (as defined below) of the Company, (vii) purchase contracts (the “Purchase Contracts”) of the Company with respect to Securities of the Company or securities of an unaffiliated entity, and (viii) units (the “Units”, and, together with the Common Shares, the Preferred Shares, the Depositary Shares, the Debt Securities, the Warrants, the Rights and the Purchase Contracts, the “Securities”).

This opinion letter is given in accordance with the terms of the Validity of Securities section of the Registration Statement.

1Documents Reviewed

We have reviewed originals, copies, drafts or conformed copies of the following documents:

1.1The public records of the Company on file and available for public inspection at the Registry of Corporate Affairs in the British Virgin Islands (the “Registry of Corporate Affairs”) on 29

September 2023, including the Company’s Certificate of Incorporation and the memorandum and articles of association registered on 30 September 2022 (the “Memorandum and Articles”).

1.2The records of proceedings available from a search of the electronic records maintained on the Judicial Enforcement Management System from 1 January 2000 and available for inspection on 29 September 2023 at the British Virgin Islands High Court Registry (the “High Court Registry”).

1.3The written resolutions of the board of directors of the Company dated 2 October 2023 (the “Resolutions”).

1.4A Certificate of Incumbency dated 29 September 2023, issued by Maples Corporate Services (BVI) Limited, the Company’s registered agent (the “Registered Agent’s Certificate”).

1.5A certificate of good standing with respect to the Company issued by the Registrar of Corporate Affairs dated 29 September 2023 (the “Certificate of Good Standing”).

1.6A certificate from a director of the Company (the “Director’s Certificate”).

1.7The Registration Statement.

2Assumptions

The following opinions are given only as to, and based on, circumstances and matters of fact existing and known to us on the date of this opinion letter. These opinions only relate to the laws of the British Virgin Islands which are in force on the date of this opinion letter. In giving the following opinions we have relied (without further verification) upon the completeness and accuracy, as at the date of this opinion letter, of the Registered Agent’s Certificate, the Director’s Certificate and the Certificate of Good Standing. We have also relied upon the following assumptions, which we have not independently verified:

2.1The creation and issuance of the Preferred Shares has been, or will be, authorised and approved by the directors of the Company and, prior to the issuance of any such Preferred Shares, an appropriate amendment to, or restatement of the Memorandum and Articles to create the Preferred Shares (including all rights attaching thereto) has been registered by the Registrar of Corporate Affairs in the British Virgin Islands, for the avoidance of doubt, any such amendment to the Memorandum and Articles shall not affect the opinions set out below (the “Amended Memorandum and Articles”).

2.2The indenture to be entered into by the Company and any trustee pursuant to which the Debt Securities will be issued (the “Indenture”), the Debt Securities, the deposit agreements to be entered into between the Company and the financial institutions designated as depositaries thereunder pursuant to which the Depositary Shares will be issued (the “Deposit Agreements”), the Depositary Shares, the Warrants, the warrant agreements to be entered into between the Company and the financial institutions designated as warrant agent thereunder pursuant to which the Warrants will be issued (the “Warrant Agreements”), the Rights, the rights agreements to be entered into by the Company and the financial institutions designated as rights agent thereunder pursuant to which the Rights will be issued (the “Rights Agreements”),the Purchase Contracts, the Units and the unit agreements to be entered into by the Company pursuant to which the Units will be issued (the “Unit Agreements”, together with the Indenture, the Deposit Agreements, the Warrant Agreements, the Rights Agreements, the Purchase Agreements, the Unit Agreements and any certificates evidencing the Warrants, the Rights or the Units, the “Agreements”) have

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been, or will be, authorised and duly executed and unconditionally delivered by or on behalf of all relevant parties in accordance with all relevant laws.

2.3The Securities (other than the Shares) and the Agreements are governed by the laws of the State of New York.

2.4The Securities (other than the Shares) and the Agreements are, or will be, legal, valid, binding and enforceable against all relevant parties in accordance with their terms under the laws of the State of New York and all other relevant laws.

2.5The choice of the laws of the State of New York as the governing law of the Securities (other than the Shares) and the Agreements has, or will have, been made in good faith and would be regarded as a valid and binding selection which will be upheld by the courts of the State of New York and any other relevant jurisdiction (other than the laws of the British Virgin Islands) as a matter of the laws of the State of New York and all other relevant laws (other than the laws of the British Virgin Islands).

2.6The capacity, power, authority and legal right of all parties under all relevant laws and regulations (other than, with respect to the Company, the laws and regulations of the British Virgin Islands) to enter into, execute, unconditionally deliver and perform their respective obligations under the Securities (other than the Shares) and the Agreements.

2.7Any Securities (other than the Shares) will be issued and authenticated in accordance with the provisions of all relevant duly authorised, executed and delivered Agreement.

2.8The Securities (other than the Shares) and the Agreements will be, or have been, duly executed and delivered by an authorised person of the parties thereto.

2.9There is no contractual or other prohibition or restriction (other than as arising under British Virgin Islands law) binding on the Company prohibiting or restricting it from entering into and performing its obligations under Securities (other than the Shares) and the Agreements.

2.10No monies paid to or for the account of any party under the Agreements represent or will represent proceeds of criminal conduct (as defined in the Proceeds of Criminal Conduct Act (As Revised)).

2.11The issue of the Securities and entry into the Agreements will be of commercial benefit to the Company.

2.12Copies of documents, conformed copies or drafts of documents provided to us are true and complete copies of, or in the final forms of, the originals.

2.13All signatures, initials and seals are genuine.

2.14The Debt Securities will be issued and authenticated in accordance with the provisions of a duly authorised, executed and delivered Indenture.

2.15That all public records of the Company which we have examined are accurate and that the information disclosed by the searches which we conducted against the Company at the Registry of Corporate Affairs and the High Court Registry is true and complete and that such information has not since then been altered and that such searches did not fail to disclose any information which had been delivered for registration but did not appear on the public records at the date of our searches.

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2.16The Memorandum and Articles remain in full force and effect and are unamended other than in the case of Preferred Shares being issued under the Amended Memorandum and Articles. There will be sufficient Shares authorised for issue under the Memorandum and Articles or Amended Memorandum and Articles, as appropriate.

2.17The Resolutions passed at any meeting of the board of directors of the Company are a true and correct record of the proceedings of a meeting of the board of directors of the Company, which was duly convened and held, and at which a quorum was present throughout and at which each director disclosed his interest (if any), in the manner prescribed in the Memorandum and Articles, and the resolutions passed at such meeting have not been amended, varied or revoked in any respect. The written resolutions of the board of directors dated 2 October 2023 were signed by all the directors in the manner prescribed in the Memorandum and Articles of the Company, including as to the disclosure of any director’s interests, and have not been amended, varied or revoked in any respect.

2.18The members of the Company (the “Members”) have not restricted or limited the powers of the directors of the Company in any way.

2.19The Company has sufficient authorised and unissued Shares under the Memorandum and Articles at the time any Shares are issued.

2.20No invitation has been or will be made by or on behalf of the Company to the public in the British Virgin Islands to subscribe for any of the Securities.

2.21The Company has received, or will receive, cash consideration or non-cash consideration in consideration for the issue of the Shares, and that:

(a)none of the Shares have been, or will be, issued for less than their par value; and

(b)to the extent that any Shares are, or will be, issued, in whole or in part, for non-cash consideration, the value of the non-cash consideration and cash consideration, if any, is not less than the amount credited or to be credited for such Shares.

2.22The Shares to be issued upon exchange or conversion of the Debt Securities or exercise of the Warrants or Rights are issued for cash consideration, or, to the extent that any Shares to be issued upon exchange or conversion of the Debt Securities or exercise of the Warrants or Rights are to be issued, in whole or in part, for non-cash consideration, the Company has passed or will pass a resolution of directors in respect of such Shares stating:

(a)the amount to be credited for the issue of such Shares; and

(b)that, in their opinion, the present cash value of the non-cash consideration and cash consideration, if any, is not less than the amount to be credited for such Shares.

2.23There is nothing under any law (other than the laws of the British Virgin Islands) which would or might affect the opinions set out below. We have not made any investigation of the laws, rules or regulations of any jurisdiction other than the laws of the British Virgin Islands.

Save as aforesaid we have not been instructed to undertake and have not undertaken any further enquiry or due diligence in relation to the transaction the subject of this opinion.

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3.Opinions

Based upon, and subject to, the foregoing assumptions and the qualifications set out below, and having regard to such legal considerations as we deem relevant, we are of the opinion that:

3.1The Company is a company limited by shares incorporated with limited liability under the BVI Business Companies Act (As Revised) (the “Act”), is in good standing at the Registry of Corporate Affairs, is validly existing under the laws of the British Virgin Islands and possesses the capacity to sue and be sued in its own name.

3.2With respect to the Common Shares, when: (a) the board of directors of the Company has taken all necessary corporate action to approve the issue thereof, the terms of the offering thereof and related matters; (b) the issue of such Common Shares have been recorded in the Company’s register of members; and (c) the subscription price of such Common Shares have been fully paid in cash or other consideration approved by the board of directors of the Company, the Common Shares will be duly authorised, validly issued, fully-paid and non-assessable. As a matter of British Virgin Islands law, a share is only issued when it has been entered in the register of members.

3.3The Company has all the requisite power and authority under the Memorandum and Articles to enter into, execute and perform its obligations under:

(a)the Indenture to which it will be a party and the Debt Securities issuable under such Indenture to which it is, or will be, a party;

(b)each Deposit Agreement to which it will be a party and the Depositary Shares issuable under each such Deposit Agreement to which it is, or will be, a party;

(c)each Warrant Agreement to which it will be a party and the Warrants issuable under each such Warrant Agreement to which will be a party;

(d)each Rights Agreement to which it will be a party and the Rights issuable under each such Rights Agreement to which will be a party;

(e)each Purchase Contract to which it will be a party; and

(f)each Unit Agreement to which it will be a party and the Units issuable under each such Unit Agreement to which will be a party.

3.4With respect to the Preferred Shares, when (i) the board of directors of the Company has taken all necessary corporate action to approve the issue thereof, the terms of the offering thereof and related matters; (ii) the Amended Memorandum and Articles have been registered by the Registrar of Corporate Affairs in the British Virgin Islands, (iii) the issue of such Preferred Shares has been recorded in the Company’s register of members, and (iv) the subscription price of such Preferred Shares (being not less than the par value of the Preferred Shares) has been fully paid in cash or other consideration approved by the board of directors of the Company, the Preferred Shares will be duly authorised, validly issued, fully paid and non-assessable.

3.5With respect to each issue of Debt Securities pursuant to the Indenture, when (i) the board of directors of the Company has taken all necessary corporate action to approve the issue thereof, the terms of the offering thereof and related matters; (ii) the Indenture relating to the Debt Securities shall have been duly authorised and validly executed and delivered by the Company and the trustee thereunder; and (iii) when such Debt Securities issued thereunder have been duly executed and delivered on behalf of the Company and authenticated in the

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manner set forth in the Indenture relating to such issue of Debt Securities and delivered against due payment therefor pursuant to, and in accordance with, the terms of the Registration Statement and any relevant prospectus supplement, such Indenture and the Debt Securities issued pursuant to the Indenture will have been duly executed, issued and delivered.

3.6With respect to the Deposit Agreements and the Depositary Shares, when (i) the board of directors of the Company has taken all necessary corporate action to approve the creation and terms of the Depositary Shares and to approve the issue thereof, the terms of the offering thereof and related matters; (ii) a Deposit Agreement relating to the Depositary Shares shall have been duly authorised and validly executed and delivered by the Company and the financial institution designated as depositary thereunder; and (iii) the certificates representing the Depositary Shares have been duly executed, countersigned, registered and delivered in accordance with the Deposit Agreement relating to the Depositary Shares and the applicable definitive purchase, underwriting or similar agreement approved by the board of directors of the Company upon payment of the consideration therefor provided therein, the Deposit Agreements and the Depositary Shares issued thereunder will be duly authorised, legal and binding obligations of the Company.

3.7With respect to the Warrant Agreements and the Warrants, when (i) the board of directors of the Company has taken all necessary corporate action to approve the creation and terms of the Warrants and to approve the issue thereof, the terms of the offering thereof and related matters; (ii) a Warrant Agreement relating to the Warrants shall have been duly authorised and validly executed and delivered by the Company and the financial institution designated as warrant agent thereunder; and (iii) the certificates representing the Warrants have been duly executed, countersigned, registered and delivered in accordance with the Warrant Agreement relating to the Warrants and the applicable definitive purchase, underwriting or similar agreement approved by the board of directors of the Company upon payment of the consideration therefor provided therein, the Warrant Agreements and the Warrants issued thereunder will be duly authorised, legal and binding obligations of the Company.

3.8With respect to the Rights Agreements and the Rights, when (i) the board of directors of the Company has taken all necessary corporate action to approve the creation and terms of the Rights and to approve the issue thereof, the terms of the offering thereof and related matters; (ii) a Rights Agreement relating to the Rights shall have been duly authorised and validly executed and delivered by the Company and the financial institution designated as rights agent thereunder; and (iii) the certificates representing the Rights have been duly executed, countersigned, registered and delivered in accordance with the Rights Agreement relating to the Rights and the applicable definitive purchase, underwriting or similar agreement approved by the board of directors of the Company upon payment of the consideration therefor provided therein, the Rights Agreements and the Rights issued thereunder will be duly authorised, legal and binding obligations of the Company.

3.9With respect to the Purchase Contracts, when a Purchase Contract shall have been duly authorised and validly executed and delivered by the Company and other parties thereto, such Purchase Contract will be duly authorised, legal and binding obligations of the Company. With respect to the Unit Agreements and the Units, when (i) the board of directors of the Company has taken all necessary corporate action to approve the creation and terms of the Units and to approve the issue thereof, the terms of the offering thereof and related matters; and (ii) a Unit Agreement relating to the Units shall have been duly authorised and validly executed and delivered by the Company and other parties thereto; and (iii) the certificates representing the Units have been duly executed, countersigned, registered and

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delivered in accordance with the Unit Agreement relating to the Units and the applicable definitive purchase, underwriting or similar agreement approved by the board of directors of the Company upon payment of the consideration therefor provided therein, the Unit Agreements and the Units issued thereunder will be duly authorised, legal and binding obligations of the Company.

3.10With respect to the Unit Agreements and the Units, when (i) the board of directors of the Company has taken all necessary corporate action to approve the creation and terms of the Units and to approve the issue thereof, the terms of the offering thereof and related matters; (ii) a Unit Agreement relating to the Units shall have been duly authorised and validly executed and delivered by the Company and other parties thereto; and (iii) the certificates representing the Units have been duly executed, countersigned, registered and delivered in accordance with the Unit Agreement relating to the Units and the applicable definitive purchase, underwriting or similar agreement approved by the board of directors of the Company upon payment of the consideration therefor provided therein, the Unit Agreements and the Units issued thereunder will be duly authorised, legal and binding obligations of the Company.

3.11With respect to any Shares to be resold by the selling shareholders as contemplated by the Registration Statement, when (a) the board of directors of the Company has taken all necessary corporate action to approve the issue thereof, the terms of the offering thereof and related matters; (b) the issue of such Shares have been recorded in the Company’s register of members; and (c) the subscription price of such Shares have been fully paid in cash or other consideration approved by the board of directors of the Company, such Shares will be duly authorised, validly issued, fully-paid and non-assessable. As a matter of British Virgin Islands law, a share is only issued when it has been entered in the register of members.

4Qualifications

The opinions expressed above are subject to the following qualifications:

4.1We have not reviewed the Agreements or the terms of the Securities (other than the Common Shares) and our opinions are qualified accordingly.

4.2The obligations assumed by the Company under the Agreements and the issuance of the Securities thereunder will not necessarily be enforceable in all circumstances in accordance with their terms. In particular:

(a)enforcement may be limited by bankruptcy, insolvency, liquidation, reorganisation, readjustment of debts or moratorium or other laws of general application relating to or affecting the rights of creditors;

(b)enforcement may be limited by general principles of equity. For example, equitable remedies such as specific performance may not be available, inter alia, where damages are considered to be an adequate remedy;

(c)some claims may become barred under relevant statutes of limitation or may be or become subject to defences of set off, counterclaim, estoppel and similar defences;

(d)where obligations are to be performed in a jurisdiction outside the British Virgin Islands, they may not be enforceable in the British Virgin Islands to the extent that performance would be illegal under the laws of that jurisdiction;

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(e)the courts of the British Virgin Islands have jurisdiction to give judgment in the currency of the relevant obligation;

(f)arrangements that constitute penalties will not be enforceable;

(g)enforcement may be prevented by reason of fraud, coercion, duress, undue influence, misrepresentation, public policy or mistake or limited by the doctrine of frustration of contracts;

(h)an agreement made by a person in the course of carrying on unauthorised financial services business is unenforceable against the other party under section 50F of the Financial Services Commission Act, 2001;

(i)provisions imposing confidentiality obligations may be overridden by compulsion of applicable law or the requirements of legal and/or regulatory process;

(j)the courts of the British Virgin Islands may decline to exercise jurisdiction in relation to substantive proceedings brought under or in relation to the Agreements in matters where they determine that such proceedings may be tried in a more appropriate forum;

(k)a person who is not a party to an Agreement that is governed by British Virgin Islands law will not have the benefit of and will not be able to enforce its terms;

(l)any provision of an Agreement that is governed by British Virgin Islands law which expresses any matter to be determined by future agreement may be void or unenforceable;

(m)we reserve our opinion as to the enforceability of the relevant provisions of an Agreement to the extent that it purports to grant exclusive jurisdiction as there may be circumstances in which the courts of the British Virgin Islands would accept jurisdiction notwithstanding such provisions; and

(n)a company cannot, by agreement or in its articles of association, restrict the exercise of a statutory power and there is doubt as to the enforceability of any provision in the Agreements whereby the Company covenants to restrict the exercise of powers specifically given to it under the Act including, without limitation, the power to increase its maximum number of shares, amend its memorandum and articles of association or present a petition to a British Virgin Islands court for an order to wind up the Company.

4.3Applicable court fees will be payable in respect of enforcement of the Agreements.

4.4To maintain the Company in good standing with the Registrar of Corporate Affairs under the laws of the British Virgin Islands, annual filing fees must be paid and returns made to the Registrar of Corporate Affairs within the time frame prescribed by law.

4.5Preferred creditors under British Virgin Islands law will rank ahead of unsecured creditors of the Company. Furthermore, all costs, charges and expenses properly incurred in the winding up of a company, including the remuneration of the liquidators, are payable out of the assets of the company in priority to all other unsecured claims.

4.6The obligations of the Company may be subject to restrictions pursuant to United Nations and United Kingdom sanctions extended to the British Virgin Islands by Orders in Council

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and/or sanctions imposed by governmental or regulatory authorities or agencies in the British Virgin Islands under British Virgin Islands legislation.

4.7A certificate, determination, calculation or designation of any party to an Agreement as to any matter provided therein might be held by a British Virgin Islands court not to be conclusive final and binding if, for example, it could be shown to have an unreasonable or arbitrary basis, or in the event of manifest error

4.8We reserve our opinion as to the extent to which the courts of the British Virgin Islands would, in the event of any relevant illegality or invalidity, sever the relevant provisions of an Agreement and enforce the remainder of the Agreement or the transaction of which such provisions form a part, notwithstanding any express provisions in an Agreement in this regard.

4.9We express no opinion as to the meaning, validity or effect of any references to foreign (i.e. non-British Virgin Islands) statutes, rules, regulations, codes, judicial authority or any other promulgations and any references to them in an Agreement.

4.10Under British Virgin Islands law, the register of members is prima facie evidence of title to shares and this register would not record a third party interest in such shares. However, there are certain limited circumstances where an application may be made to a British Virgin Islands court for a determination on whether the register of members reflects the correct legal position. Further, the British Virgin Islands court has the power to order that the register of members maintained by a company should be rectified where it considers that the register of members does not reflect the correct legal position. There are no circumstances or matters of fact known to us on the date of this opinion letter which would properly form the basis for an application for an order for rectification of the register of members of the Company, but if such an application were made in respect of the Shares, then the validity of such shares may be subject to re-examination by a British Virgin Islands court.

4.11In this opinion letter, the phrase “non-assessable” means, with respect to the issuance of shares, that a shareholder shall not, in respect of the relevant shares and in the absence of a contractual arrangement, or an obligation pursuant to the memorandum and articles of association, to the contrary, have any obligation to make further contributions to the Company’s assets (except in exceptional circumstances, such as involving fraud, the establishment of an agency relationship or an illegal or improper purpose or other circumstances in which a court may be prepared to pierce or lift the corporate veil).

4.12We express no view as to the commercial terms of the Securities or the Agreements or whether such terms represent the intentions of the parties and we make no comment with respect to any representations and warranties which may be made by or with respect to the Company in any of the documents or instruments cited in this opinion or otherwise with respect to the commercial terms of the transactions the subject of this opinion.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference to our firm under the heading “Validity of Securities” in the prospectus included in the Registration Statement. In providing our consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the SEC Act or the rules and regulations of the Commission thereunder.

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This opinion is addressed to you and may be relied upon by you, your counsel and purchasers of Securities pursuant to the Registration Statement. This opinion is limited to the matters detailed herein and is not to be read as an opinion with respect to any other matter.

Yours faithfully

/s/ Maples and Calder

Maples and Calder

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