Exhibit 5.1

Chrysler Center 919 Third Avenue New York, NY 10022 212 935 3000 mintz.com

May 17, 2023

Acurx Pharmaceuticals, Inc.

259 Liberty Avenue

Staten Island, New York 10305 

Ladies and Gentlemen:

We have acted as counsel to Acurx Pharmaceuticals, Inc., a Delaware corporation (the “Company”), in connection with the preparation and filing with the Securities and Exchange Commission (the “Commission”) of a Prospectus Supplement, dated May 16, 2023, to a Prospectus, dated July 11, 2022 (the “Prospectus and Prospectus Supplement”), filed pursuant to a Registration Statement on Form S-3, Registration No. 333-265956 (the “Registration Statement”) and filed by the Company with the Commission under the Securities Act of 1933, as amended (the “Securities Act”). The Prospectus Supplement relates to the sale of (a) 601,851 shares (the “Shares”) of the Company’s common stock, $0.001 par value per share (the “Common Stock”) and (b) pre-funded warrants (the “Pre-Funded Warrants”) to purchase up to 731,482 shares of Common Stock (the “Warrant Shares” and collectively with the Shares and the Pre-Funded Warrants, the “Securities”), pursuant to a Securities Purchase Agreement, dated May 16, 2023, between the Company and the purchasers named therein (the “Purchase Agreement”). The Purchase Agreement will be filed as an exhibit to a Current Report on Form 8-K and incorporated by reference into the Registration Statement. This opinion is being rendered in connection with the filing of the Prospectus Supplement with the Commission. All capitalized terms used herein and not otherwise defined shall have the respective meanings given to them in the Registration Statement.

In connection with this opinion, we have (i) examined and relied upon: (A) the Registration Statement, the Prospectus and the Prospectus Supplement, (B) the form of Pre-Funded Warrant to be filed as an exhibit to the Registration Statement, (C) the Company’s Certificate of Incorporation and Amended and Bylaws, as currently in effect, and (D) the originals or copies certified to our satisfaction of such records, documents, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below; and (ii) assumed that the Securities to be sold by the Company will be sold at a price and on terms established by the Board of Directors of the Company or a duly constituted pricing committee thereof in accordance with Section 153 of the Delaware General Corporation Law. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not independently verified such matters. In rendering this opinion, we have assumed the genuineness and authenticity of all signatures on signed documents; the authenticity of all documents submitted to us as originals; the conformity to originals of all documents submitted to us as copies; the accuracy, completeness and authenticity of certificates of public officials; and the due authorization, execution and delivery of all documents where due authorization, execution and delivery are a prerequisite to the effectiveness thereof (except we have not made such assumption with respect to the Company).

MINTZ   May 17, 2023 Page 2

Our opinion is limited to the General Corporation Law of the State of Delaware and, as to the Pre-Funded Warrants constituting valid and binding obligations of the Company, the laws of the State of New York, and we express no opinion with respect to the laws of any other jurisdiction. No opinion is expressed herein with respect to the qualification of the Shares under the securities or blue sky laws of any state or any foreign jurisdiction.

With regard to our opinion concerning the Pre-Funded Warrants constituting valid and binding obligations of the Company:

(i) Our opinion is subject to, and may be limited by, (a) applicable bankruptcy, reorganization, insolvency, moratorium, fraudulent conveyance, debtor and creditor, and similar laws which relate to or affect creditors’ rights generally, and (b) general principles of equity (including, without limitation, concepts of materiality, reasonableness, good faith and fair dealing) regardless of whether considered in a proceeding in equity or at law.

(ii) Our opinion is subject to the qualification that the availability of specific performance, an injunction or other equitable remedies is subject to the discretion of the court before which the request is brought.

(iii) We express no opinion as to any provision of the Pre-Funded Warrants that: (a) provides for liquidated damages, buy-in damages, monetary penalties, prepayment or make-whole payments or other economic remedies to the extent such provisions may constitute unlawful penalties, (b) relates to advance waivers of claims, defenses, rights granted by law, or notice, opportunity for hearing, evidentiary requirements, statutes of limitations, trial by jury, or procedural rights, (c) restricts non-written modifications and waivers, (d) provides for the payment of legal and other professional fees where such payment is contrary to law or public policy, (e) relates to exclusivity, election or accumulation of rights or remedies, or (f) provides that provisions of the Pre-Funded Warrants are severable to the extent an essential part of the agreed exchange is determined to be invalid and unenforceable.

(iv) We express no opinion as to whether a state court outside of the State of New York or a federal court of the United States would give effect to the choice of New York law provided for in the Pre-Funded Warrants.

MINTZ   May 17, 2023 Page 3

With respect to the Warrant Shares, we express no opinion to the extent that, notwithstanding its current reservation of shares of Common Stock, future issuances of securities, including the Warrant Shares, of the Company and/or adjustments to outstanding securities, including the Pre-Funded Warrants, of the Company may cause the Pre-Funded Warrants to be exercisable for more shares of Common Stock than the number that remain authorized but unissued. Further, we have assumed the Exercise Price (as defined in the Pre-Funded Warrants) will not be adjusted to an amount below the par value per share of the Common Stock.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that (i) the Shares, when sold and issued in accordance with the Registration Statement, the Prospectus and the Prospectus Supplement, will be validly issued, fully paid and nonassessable, (ii) provided that the Pre-Funded Warrants have been duly executed and delivered by the Company and duly delivered to the purchasers thereof against payment therefor, the Pre-Funded Warrants, when sold and issued as contemplated in the Registration Statement, the Prospectus and the Prospectus Supplement, will be valid and binding obligations of the Company, and (iii) the Warrant Shares, when issued and paid for in accordance with the terms of the Pre-Funded Warrants, will be validly issued, fully paid and non-assessable.

We hereby consent to the filing of this opinion as an exhibit to a Current Report on Form 8-K in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act and to the use of this Firm’s name therein and in the Prospectus Supplement under the caption “Legal Matters.” In giving such consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.