Exhibit 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Annual Report of Incannex Healthcare Inc., (the “Company”) on Form 10-K for the fiscal year ended June 30, 2024, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I certify in my capacity as the principal executive officer of the Company, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that, to the best of my knowledge:

(1) The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and result of operations of the Company.

Date: September 30, 2024	By:	/s/ Joel Latham
		Joel Latham
		Chief Executive Officer and President (principal executive officer)