Exhibit 5.1

Faegre Drinker Biddle & Reath LLP

2200 Wells Fargo Center
90 S. Seventh Street
Minneapolis, Minnesota 55402

+1 612 766 7000 main

+1 612 766 1600 fax

July 31, 2025

Celcuity Inc.

16305 36^th Avenue North, Suite 100

Minneapolis, Minnesota 55446

Ladies and Gentlemen:

We have acted as counsel to Celcuity Inc., a Delaware corporation (the “Company”), in connection with the public offering by the Company of (a) 2,172,368 shares (the “Shares”) of common stock, par value $0.001 per share (the “Common Stock”) or pre-funded warrants to purchase shares of Common Stock (the “Pre-Funded Warrants”), and (b) up to 400,000 shares of Common Stock issuable from time to time upon exercise of the Pre-Funded Warrants (the “Warrant Shares” and, together with the Pre-Funded Warrants and the Shares, the “Securities”). The Securities are being offered pursuant to the Registration Statement on Form S-3 (Registration No. 333-281887) filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), on August 30, 2024, as amended (as so filed and as amended, the “Registration Statement”), the base prospectus, dated December 2, 2024, included in the Registration Statement at the time it originally became effective (the “Base Prospectus”), the preliminary prospectus supplement, dated July 28, 2025, filed with the Commission pursuant to Rule 424(b) under the Act (together with the Base Prospectus, the “Preliminary Prospectus Supplement”), and the final prospectus supplement, dated July 30, 2025, filed with the Commission pursuant to Rule 424(b) under the Act (together with the Base Prospectus, the “Prospectus”). The Securities are being sold pursuant to an underwriting agreement, dated as of July 30, 2025, by and among Jefferies LLC, TD Securities (USA) LLC, and Leerink Partners LLC, as representatives of the several underwriters listed on Schedule A thereto, and the Company (the “Underwriting Agreement”).

This opinion is being furnished in connection with the requirements of Item 601(b)(5) of Regulation S-K under the Act.

In rendering the opinions expressed herein, we have examined or are otherwise familiar with the Certificate of Incorporation of the Company, as amended to the date hereof, and the Bylaws of the Company, as amended to the date hereof, and we have reviewed originals, or copies certified or otherwise authenticated to our satisfaction, of (i) the Registration Statement, (ii) the Preliminary Prospectus Supplement, (iii) the Prospectus, (iv) the Underwriting Agreement, (v) the form of Pre-Funded Warrant filed as Exhibit 4.1 to the Current Report on Form 8-K filed by the Company with the Commission on the date hereof and (vi) the corporate actions taken by the Company in connection with the authorization of the Underwriting Agreement and the Securities. We have also examined originals, or copies certified or otherwise authenticated to our satisfaction, of such corporate records of the Company and other instruments, certificates of public officials and representatives of the Company, and other documents as we have deemed necessary as a basis for the opinions hereinafter expressed and have made such examination of statutes and decisions and reviewed such questions of law as we have considered necessary or appropriate for the purposes of this opinion letter.

Based on and subject to the foregoing and to the other assumptions, qualifications and limitations set forth herein, we are of the opinion that:

1. The issuance and sale of the Shares have been duly authorized by all corporate action on the part of the Company and, (a) when the Shares have been issued by the Company against payment of the agreed-upon consideration therefor in accordance with the terms of the Underwriting Agreement, and (b) upon the due registration of issuance and constructive delivery through book entry of such Shares by the transfer agent and registrar therefor in the name or on behalf of the purchasers thereof, then, upon the happening of such events, such Shares will be validly issued, fully paid and non-assessable.

July 31, 2025

Page 2

2. The issuance and sale of the Pre-Funded Warrants have been duly authorized by all corporate action on the part of the Company and when the Pre-Funded Warrants have been duly executed and delivered by the Company to the purchasers thereof against payment therefor as provided in resolutions adopted by the Company’s Board of Directors and its Pricing Committee, and in accordance with the Underwriting Agreement, the Registration Statement and the Prospectus, the Pre-Funded Warrants will be valid and binding obligations of the Company, except as the same may be limited by applicable bankruptcy, insolvency, voidable transaction, fraudulent conveyance, fraudulent transfer, reorganization, moratorium, assignment for the benefit of creditors and other laws relating to or affecting creditors’ rights generally and equitable principles of general applicability (regardless of whether considered in a proceeding in equity or at law).

3. All necessary action on the part of the Company has been taken to authorize the issuance of the Warrant Shares, and (a) when the Pre-Funded Warrants have been duly executed and delivered by the Company to the purchasers thereof against payment therefor as provided in resolutions adopted by the Company’s Board of Directors and its Pricing Committee, and in accordance with the Underwriting Agreement, the Registration Statement and the Prospectus, and (b) when any Warrant Shares are issued by the Company upon due and proper exercise of the Pre-Funded Warrants by the applicable holder thereof in accordance with the terms of the Pre-Funded Warrants, including the receipt by the Company of the exercise price therefor as specified in the Pre-Funded Warrants, and (c) upon the due registration of issuance and constructive delivery through book entry of such Warrant Shares by the transfer agent and registrar therefor, then, upon the happening of such events, such Warrant Shares will be validly issued, fully paid and non-assessable.

We have relied upon certificates of public officials as to the accuracy of all matters addressed therein and, with respect to certain factual matters, upon certificates of and information provided by officers and employees of the Company as to the accuracy of such factual matters, in each case without independent verification thereof or other investigation. We have assumed, without investigation, the following: (a) the genuineness of signatures, including electronic signatures, appearing upon the certifications, documents, and proceedings submitted to us for review, (b) that each document submitted to us for review is accurate and complete, each such document that is an original is authentic and each such document that is a copy conforms to an authentic original, (c) the legal capacity of natural persons who are involved on behalf of the Company to enter into and perform the referenced instrument or agreement or to carry out their role in the transactions contemplated thereby, (d) the truth, accuracy and completeness of the information, representations and warranties contained in the documents, instruments, certificates and records we have reviewed, (e) the absence of any undisclosed modifications to the agreements and instruments reviewed by us, and (f) the Company will comply with all applicable notice requirements regarding uncertificated shares provided in the General Corporation Law of the State of Delaware.

Without limiting any other qualifications set forth herein, the opinion expressed herein regarding the enforceability of the Pre-Funded Warrants is subject to the effect of generally applicable laws that (i) provide for the enforcement of oral waivers or modifications where a material change of position in reliance thereon has occurred or provide that a course of performance may operate as a waiver; (ii) limit the availability of a remedy under certain circumstances where another remedy has been elected; (iii) limit the enforceability of provisions releasing, exculpating or exempting a party from, or requiring indemnification of a party for, liability for its own action or inaction, to the extent the action or inaction involves negligence, recklessness, willful misconduct or unlawful conduct; (iv) may, where less than all of a contract may be unenforceable, limit the enforceability of the balance of the contract to circumstances in which the unenforceable portion is not an essential part of the agreed exchange; (v) govern and afford judicial discretion regarding the determination of damages and entitlement to attorneys’ fees and other costs; (vi) may permit a party who has materially failed to render or offer performance required by a contract to cure that failure unless either permitting a cure would unreasonably hinder the aggrieved party from making substitute arrangements for performance or it is important under the circumstances to the aggrieved party that performance occur by the date stated in the contract; (vii) may require mitigation of damages; (viii) provide a time limitation after which a remedy may not be enforced (i.e., statutes of limitation); and (ix) limit the enforceability of provisions of instruments or agreements that purport to require waiver of the obligations of good faith, fair dealing, diligence and reasonableness.

July 31, 2025

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We express no opinion as to the enforceability or effect in the Pre-Funded Warrants of (i) any agreement to submit to the jurisdiction of any particular court or other governmental authority (either as to personal jurisdiction or subject matter jurisdiction), any provision restricting access to courts (including without limitation agreements to arbitrate disputes), any waivers of the right to jury trial, any waivers of service of process requirements that would otherwise be applicable, any agreement that a judgment rendered by a court in one jurisdiction may be enforced in another jurisdiction, or any provision otherwise affecting the jurisdiction or venue of courts; (ii) any provision waiving legal, statutory or equitable defenses or other procedural, judicial or substantive rights; or (iii) any provision that authorizes one party to act as attorney-in-fact for another party.

With respect to our opinion regarding the Warrant Shares, we express no opinion to the extent that, notwithstanding the Company’s current reservation of the maximum number of Warrant Shares as of the date hereof, future issuances of securities of the Company, including the Warrant Shares, and/or antidilution adjustments to outstanding securities of the Company, including the Pre-Funded Warrants, may cause the Pre-Funded Warrants to be exercisable for more shares of Common Stock than the number that then 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 Warrant Shares.

This opinion is limited to the General Corporation Law of the State of Delaware and, solely with respect to opinion paragraph 2, the laws of the State of New York.

This opinion letter is rendered as of the date first written above, and we assume no responsibility for updating this opinion letter or the opinions set forth herein to take into account any event, action, interpretation or change in law or facts occurring subsequent to the date hereof that may affect the validity of such opinions. This opinion letter is expressly limited to the matters set forth above, and we render no opinion, whether by implication or otherwise, as to any other matters relating to the Company or the Securities. In addition, we express no opinion as to whether, or the extent to which, the laws of any particular jurisdiction apply to the subject matter hereof, including, without limitation, the enforceability of the governing law provision contained in the Pre-Funded Warrants.

We hereby consent to the filing of this opinion letter as an exhibit to the Current Report on Form 8-K of the Company filed with the Commission on the date hereof and thereby incorporated by reference into the Registration Statement and to being named in the Prospectus included therein under the caption “Legal Matters” with respect to matters stated therein. 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 with respect to any part of the Registration Statement, including this opinion letter.

Very truly yours,

/s/ Faegre Drinker Biddle & Reath LLP

Faegre Drinker Biddle & Reath LLP