EX-5.1

Re: Registration Statement on Form S-1 (No. 333-275443); 14,255,400 shares of Common Stock, par value $0.0001 per share

We have acted as special counsel to Evoke Pharma, Inc., a Delaware corporation (the “Company”), in connection with the proposed issuance of (i) up to 14,255,400 shares (the “Shares”) of common stock, $0.0001 par value per share (the “Common Stock”), (ii) pre-funded warrants (the “Pre-Funded Warrants”) to purchase up to 12,396,000 shares of Common Stock (the “Pre-Funded Warrant Shares”) and (iii) warrants (the “Common Warrants,” and together with the Pre-Funded Warrants, the “Warrants”) to purchase up to 12,396,000 shares of Common Stock (the “Common Warrant Shares,” and together with the Pre-Funded Warrant Shares, the “Warrant Shares”). The Shares, the Warrants and the Warrant Shares are included in a registration statement on Form S-1 under the Securities Act of 1933, as amended (the “Act”), filed with the Securities and Exchange Commission (the “Commission”) on November 9, 2023 (Registration No. 333-275443) (as amended, the “Registration Statement”). The terms “Shares,” “Warrants” and “Warrant Shares” shall include any additional securities registered by the Company pursuant to Rule 462(b) under the Act in connection with the offering contemplated by the Registration Statement. This opinion is being furnished in connection with the requirements of Item 601(b)(5) of Regulation S-K under the Act, and no opinion is expressed herein as to any matter pertaining to the contents of the Registration Statement or related prospectus (the “Prospectus”), other than as expressly stated herein with respect to the issue of the Shares, the Warrants and the Warrant Shares.

As such counsel, we have examined such matters of fact and questions of law as we have considered appropriate for purposes of this letter. With your consent, we have relied upon certificates and other assurances of officers of the Company and others as to factual matters without having independently verified such factual matters. We are opining herein as to the internal laws of the State of New York and the General Corporation Law of the State of Delaware (the “DGCL”), and we express no opinion with respect to any other laws.

Subject to the foregoing and the other matters set forth herein, it is our opinion that, as of the date hereof:

When the Shares shall have been duly registered on the books of the transfer agent and registrar therefor in the name or on behalf of the purchasers and have been issued by the Company against payment therefor (not less than par value) in the circumstances contemplated by the form of underwriting agreement most recently filed as an exhibit to the Registration Statement, the issue and sale of the Shares will have been duly authorized by all necessary corporate action of the Company, and the Shares will be validly issued, fully paid and nonassessable. In rendering the foregoing opinion, we have assumed that the Company will comply with all applicable notice requirements regarding uncertificated shares provided in the DGCL.

When the Warrants shall have been issued by the Company against payment therefor in the circumstances contemplated by the form of underwriting agreement most recently filed as an exhibit to the Registration Statement, the issue and sale of the

Warrants will have been duly authorized by all necessary corporate action of the Company, and the Warrants will be legally valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

When the Warrant Shares initially issuable upon exercise of the Warrants shall have been duly registered on the books of the transfer agent and registrar therefor in the name or on behalf of the Warrant holders, and have been issued by the Company against payment therefor (not less than par value) in the circumstances contemplated by the Warrants, the issue of Warrant Shares will have been duly authorized by all necessary corporate action of the Company, and will be validly issued, fully paid and nonassessable.

In rendering the foregoing opinions, we have assumed that (i) the Company will comply with all applicable notice requirements regarding uncertificated shares provided in the General Corporation Law of the State of Delaware and (ii) upon the issue of any of the Warrant Shares, the total number of shares of Common Stock issued and outstanding will not exceed the total number of shares of Common Stock that the Company is then authorized to issue under its Amended and Restated Certificate of Incorporation and by the board of directors of the Company in connection with the offering contemplated by the Registration Statement.

With your consent, we have assumed that the status of the Warrants as legally valid and binding obligations of the Company is not affected by any (i) breaches of, or defaults under, agreements or instruments, (ii) violations of statutes, rules, regulations or court or governmental orders, or (iii) failures to obtain required consents, approvals or authorizations from, or make required registrations, declarations or filings with, governmental authorities.

Our opinions are subject to: (i) the effect of bankruptcy, insolvency, reorganization, preference, fraudulent transfer, moratorium or other similar laws relating to or affecting the rights and remedies of creditors; (ii) (a) the effect of general principles of equity, whether considered in a proceeding in equity or at law (including the possible unavailability of specific performance or injunctive relief), (b) concepts of materiality, reasonableness, good faith and fair dealing, and (c) the discretion of the court before which a proceeding is brought; and (iii) the invalidity under certain circumstances under law or court decisions of provisions providing for the indemnification of or contribution to a party with respect to a liability where such indemnification or contribution is contrary to public policy. We express no opinion as to (a) any provision for liquidated damages, default interest, late charges, monetary penalties, make whole premiums or other economic remedies to the extent such provisions are deemed to constitute a penalty; (b) consents to, or restrictions upon, governing law, jurisdiction, venue, arbitration, remedies, or judicial relief; (c) any provision requiring the payment of attorneys’ fees, where such payment is contrary to law or public policy; (d) other applicable exceptions; and (e) the severability, if invalid, of provisions to the foregoing effect.

This opinion is for your benefit in connection with the Registration Statement and may be relied upon by you and by persons entitled to rely upon it pursuant to the applicable provisions of the Act. We consent to your filing this opinion as an exhibit to the Registration Statement and to the reference to our firm contained in the Prospectus under the heading “Legal Matters.” We further consent to the incorporation by reference of this letter and consent into any registration statement or post-effective amendment to the Registration Statement filed pursuant to Rule 462(b) under the Act with respect to the Shares and the Warrants. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission thereunder.