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 Quarterly Report of Incannex Healthcare Inc. (the “Company”) on Form 10-Q for the quarter ended March 31, 2024 (the “Report”) as filed with the Securities and Exchange Commission on the date hereof, I, Joel Latham, Chief Executive Officer of the Company, certify pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

1. The Report fully complies with the requirements of Section 13(a) or 15(d) of the Exchange Act, as amended; and

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

Date: May 15, 2024
By:	/s/ Joel Latham
Name:	Joel Latham
Title:	President and Chief Executive Officer (principal executive officer)