Exhibit 5.1

Orphazyme A/S

Ole Maaløes Vej 3

DK-2200 Copenhagen N

Denmark

(the “Company”)

Date: 15 October 2021

Dear Madams and Sirs,

Orphazyme A/S – Registration Statement on Form F-3 filed with the United States Securities and Exchange Commission

We have acted as Danish legal counsel to Orphazyme A/S, company reg. no. (CVR) 32 26 63 55 (the “Company”) with respect to a potential offering, issuance and sale by the Company from time to time in one or more offerings of ordinary shares with a nominal value of DKK 1 per share (the “Underlying Shares”), which may be represented by American Depositary Shares (“ADSs”), each such ADS representing one ordinary share, and any such ADSs having an aggregate offering price of up to $ 75,000,000 (the “Offering” or “Offerings”).

Any such Underlying Shares are expected to be admitted to trading and official listing on Nasdaq Copenhagen A/S (“Nasdaq Copenhagen”) and any such ADSs are expected to be listed on the Nasdaq Global Select Market in the United States (“Nasdaq Global”).

This opinion (the “Opinion”) is being furnished in connection with the registration statement, as the same may be amended from time to time, (the “Registration Statement”) on Form F-3 filed by the Company with the Securities and Exchange Commission on 15 October 2021 pursuant to the Securities Act of 1933, as amended (the “Securities Act”).

1 For the purpose of this Opinion we have examined the following documents and performed the following investigations:

a) a copy of the Registration Statement;

b) a copy of the articles of association of the Company dated 25 March 2021 (the “Articles of Association”);

c) a copy of the minutes of the annual general meeting of the Company held on 25 March 2021 whereby the annual general meeting adopted an authorization to the Board of Directors to increase the Company’s share capital without preemption rights for existing shareholders by a nominal amount of up to DKK 6,989,767;

Axel Towers, Axeltorv 2, 1609 Copenhagen V, Denmark

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d) a copy of the resolution passed by the Board of Directors of the Company on 14 October 2021 approving inter alia the Registration Statement, including a base prospectus;

e) draft resolutions whereby the Board of Directors inter alia (i) approves the issuance and offering of any such Underlying Shares and ADSs and approves the Company’s participation in the Offering, and (ii) exercises a part of the authorization in the Company’s Articles of Association to increase the Company’s share capital in connection with the offering of any such Underlying Shares and ADSs;

f) a draft copy of the subscription list to be delivered to the Company regarding subscription of any such Underlying Shares;

g) an online transcript of 15 October 2021 (before 8 pm CEST) from the Danish Business Authority (in Danish: “Erhvervsstyrelsen”) concerning the Company; and

h) such other documents, agreements and records as we have deemed necessary for the purposes of rendering this Opinion.

The documents mentioned in sections 1a) – 1h) above are referred to as the “Documents” and individually as a “Document”.

2 In considering the Documents for the purposes of delivering this Opinion we have assumed:

a) that any copies of the Documents that we have reviewed are complete and accurate copies of the originals of such Documents and that the originals of such Documents were executed in the manner appearing on such copies and that all material supplied to us (whether original or in copy) is authentic, has been supplied in full and has not subsequently been amended;

b) the genuineness of all signatures and dates and the authenticity of all documents submitted to us as originals;

c) that each Document is true, correct and fully updated and has not been amended or revoked after the date of each such Document;

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d) that all resolutions and documents will be made and finalized to effect (i) the authorization of the Board of Directors to issue any such Underlying Shares, (ii) the subscription of any such Underlying Shares, (iii) the payment in full of any such Underlying Shares, (iv) the registration of any such Underlying Shares with the Danish Business Authority, (v) the issuance in and registration with VP Securities A/S of any such Underlying Shares, and (vi) the admission to trading and official listing on Nasdaq Copenhagen of any such Underlying Shares;

e) the information contained in the online transcript dated 15 October 2021 from the Danish Business Authority (referred to in section 1g)) concerning the Company being accurate, complete and fully updated;

f) that the subscription price established for any potential offered ADSs, and by extension any such Underlying Shares, is the prevailing market price as quoted on Nasdaq Global in accordance with applicable Danish corporate law principles, for any such ADSs, and by extension any such Underlying Shares at the time of issue;

g) the genuineness of all signatures and dates on all Documents examined by us, and that the identities of the signatories are as stated or written;

h) that any power of attorney referred to in the Documents has neither been revoked nor amended;

i) that there are no provisions of the laws of any jurisdiction (other than Denmark) that would have any adverse implication in relation to the opinions expressed herein;

j) that the Company will, simultaneously with the settlement of any issued ADSs, receive payment for any such ADSs and by extension any such Underlying Shares;

k) the accuracy and completeness of all factual matters, statements of fact, factual representations, warranties and other information as to matters of fact described or set forth in the Documents, as we have not made any independent investigation in respect thereof;

l) the due compliance of all matters with and validity and binding effect under such laws as govern any activities contemplated other than the laws of Denmark in respect of which we are opining;

m) that a “corporate benefit”, as such term is construed under Danish law, will accrue to the Company from entering into any transactions related to the Documents, if relevant; and

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n) that all formalities and requirements of the laws, regulations or rules of stock exchanges of any relevant jurisdiction other than Denmark and of any regulatory authority therein, applicable to the execution, performance, delivery, perfection and enforceability of any Document have been or will be duly complied with.

3 This Opinion is subject to the following qualifications:

a) This Opinion is given only with respect to the laws of Denmark as in force today and as such laws are currently applied by Danish courts and we express no opinion with respect to the laws of any other jurisdiction nor have we made any investigations as to any law other than the laws of Denmark;

b) the ability of a Danish public limited liability company to delegate authority in general to third parties to act on its behalf is restricted pursuant to Danish law. Thus, the granting by a Danish public limited liability company of powers to third parties to act on their behalf may be considered void and set aside by the Danish courts if the powers are not restricted to specific, limited and well-defined matters and given for a certain period of time;

c) in rendering this Opinion we have relied as to certain matters of information and facts obtained from the Company and other sources reasonably believed by us to be credible;

d) we express no opinion as to the exact interpretation of any particular wording in any Document by a court;

e) the online transcript from the Danish Business Authority listed in section 1g) is not conclusive evidence of whether or not (i) a winding up or administration order has been issued, (ii) a resolution for winding up has been passed, or (iii) an administrator or liquidator has been appointed. Notice of the matters listed in (i), (ii) and (iii) in this paragraph may not be filed with the Danish Business Authority immediately and, when filed, may not be entered in the relevant company’s public file immediately. In addition, such transcripts do not report petitions for winding up or administration prior to the issuance of the order therefore; and

f) in this Opinion Danish legal concepts are expressed in English terms and not in their original Danish terms. The concepts concerned may not be identical to the concepts described by the same English terms as they exist under the laws of other jurisdictions.

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4 Based upon and subject to the assumptions and the qualifications above we are of the opinion that:

a) The Company is a public limited liability company (in Danish: “aktieselskab”) registered and validly existing under the laws of Denmark;

b) any such Underlying Shares, will upon exercise of the authorization to issue shares by the Board of Directors, subscription, payment in full, registration with the Danish Business Authority, issuance in and registration with VP Securities A/S and admission to trading and official listing on Nasdaq Copenhagen, constitute valid and fully paid shares; and

c) there are for holders of any such Underlying Shares, if fully paid in and issued, no obligation to provide additional funding pursuant to the Articles of Association or the Danish Companies Act.

We advise you that we are not assuming any obligation to notify you of any changes in this Opinion as a result of any facts or circumstances that may come to our attention in the future or as a result of any changes in laws which may hereafter occur.

This Opinion is limited to matters of the laws of Denmark (excluding Greenland and the Faroe Islands) as in effect and applied on the date of this Opinion and we express no opinion with respect to the laws of any other jurisdiction, nor have we made any investigation as to any laws other than the laws of Denmark.

This Opinion shall be governed by and construed in accordance with Danish law, and any legal suit action or proceeding against us by the Company arising out of or based upon this Opinion shall be exclusively instituted in a Danish court.

This Opinion is rendered to the Company in connection with the filing of the Registration Statement on Form F-3 and shall not be relied upon by any person other than the Company or be used by the Company for any other purpose than the filing of the Registration Statement on Form F-3.

We accept no responsibility or legal liability to any person other than the Company in relation to the contents of this Opinion and claims may only be brought against Gorrissen Federspiel Advokatpartnerselskab and not against individual partners or employees of Gorrissen Federspiel Advokatpartnerselskab on the basis hereof.

We hereby consent to the filing of this Opinion as an exhibit to the Registration Statement and to the reference to our law firm (in Danish: “Advokatpartnerselskab”) under the caption “Legal Matters” in the Registration Statement.

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In giving this consent, we do not admit that we are in the category of persons whose consent is required under section 7 of the Securities Act of 1933, as amended, and the rules and regulations promulgated thereunder.

We are qualified to practice law in Denmark.

Yours sincerely

/s/ Gorrissen Federspiel Advokatpartnerselskab