Exhibit 5.1

3580 Carmel Mountain Road, Suite 300 San Diego, CA 92130 858-314-1500 www.mintz.com

May 20, 2025

Incannex Healthcare Inc.

Suite 105, 8 Century Circuit Norwest,

NSW 2153 Australia

Ladies and Gentlemen:

We have acted as counsel to Incannex Healthcare Inc., a Delaware corporation (the “Company”), with respect to certain matters in connection with the offering by the Company of $2,514,214 of shares of the Company’s common stock, par value $0.0001 per share (the “Shares”), pursuant to the Registration Statement on Form S-3 (File No. 333-283028) (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), the related prospectus dated November 6, 2024 included within the Registration Statement (the “Base Prospectus”), and the prospectus supplement dated April 7, 2025, and prospectus supplement dated May 20, 2025, filed with the Commission pursuant to Rule 424(b) promulgated under the Act (together with the Base Prospectus, the “Prospectus”). The Shares are to be sold by the Company in accordance with that certain Sales Agreement, dated April 7, 2025, by and between the Company and A.G.P./Alliance Global Partners (the “Sales Agreement”), as described in the Prospectus.

In connection with this opinion, we have examined the Company’s Amended and Restated Certificate of Incorporation, as amended to date, and Amended and Restated Bylaws, both as currently in effect, such other records of the corporate proceedings of the Company and certificates of the Company’s officers as we have deemed relevant, as well as the Registration Statement and the exhibits thereto and the Prospectus.

In our examination, we have assumed the genuineness of all signatures, the legal capacity of natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as certified, photostatic or facsimile copies and the authenticity of the originals of such copies.

Based upon the foregoing, and subject to the limitations set forth below, we are of the opinion that the Shares, when issued by the Company out of the Company’s duly authorized common stock and issued and delivered by the Company against payment therefor as contemplated by and in accordance with the terms of the Sales Agreement, on terms approved by the Board of Directors of the Company, or a duly authorized committee thereof, will be duly and validly issued, fully paid and nonassessable.

BOSTON LOS ANGELES MIAMI NEW YORK SAN DIEGO SAN FRANCISCO TORONTO WASHINGTON

MINTZ, LEVIN, COHN, FERRIS, GLOVSKY AND POPEO, P.C.

MINTZ May 20, 2025 Page 2

Our opinion is limited to the General Corporation Law of the State of Delaware, 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.

We have relied as to certain matters on information obtained from public officials, officers of the Company, and other sources believed by us to be responsible.

Please note that we are opining only as to the matters expressly set forth herein, and no opinion should be inferred as to any other matters. This opinion is based upon currently existing statutes, rules, regulations and judicial decisions, and we disclaim any obligation to advise you of any change in any of these sources of law or subsequent legal or factual developments which might affect any matters or opinions set forth herein.

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 Act and to the use of this firm’s name therein and in the Prospectus 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 Act or the rules and regulations of the Commission.