Additional Proxy Soliciting Materials (Form DEFA14A)

UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

SCHEDULE 14A

Proxy Statement Pursuant to Section 14(a) of the Securities Exchange Act of 1934

(Amendment No. )

Check the appropriate box:

Payment of Filing Fee (Check all boxes that apply):

SUPPLEMENT TO THE PROXY STATEMENT FOR THE

ANNUAL MEETING OF STOCKHOLDERS OF

INCANNEX HEALTHCARE INC.

TO BE HELD ON JANUARY 15, 2026

This supplement, dated December 18, 2025, amends and supplements the Proxy Statement of Incannex Healthcare Inc. ("we" or the "Company"), dated October 27, 2025 (the "Proxy Statement"), relating to the 2025 annual meeting of stockholders (the "Annual Meeting"), with the following information.

Adjournment of Annual Meeting

On December 18, 2025, we announced at the Annual Meeting that there were not present or represented by proxy a sufficient number of shares of our common stock to constitute a quorum, primarily due to Proposal No. 2, relating to the ratification of the appointment of its independent registered accounting firm (the "Auditor Ratification Proposal"), being classified as a non-routine proposal because of an administrative error by the Company's transfer agent. Accordingly, we adjourned our Annual Meeting to allow for the solicitation of additional proxies with respect to the proposals set forth in the Proxy Statement. The Annual Meeting has been adjourned to Thursday, January 15, 2026, at 11:00 a.m., Gulf Standard Time, and will reconvene only virtually via live audio webcast on the Internet by visiting www.meetnow.global/MD59M9U.

We have engaged with the transfer agent and other relevant parties to seek reclassification of the Auditor Ratification Proposal and expect that the Auditor Ratification Proposal will be reclassified as routine prior to the reconvened Annual Meeting, which would permit brokers, banks, and other nominees to exercise discretionary voting authority for shares held in "street name."

During the period of the adjournment, the Company will continue to solicit proxies with respect to the proposals set forth in the Proxy Statement. Proxies previously submitted in respect of the Annual Meeting will be voted at the reconvened meeting unless properly revoked, and stockholders who have already submitted a proxy to vote their shares need not take any action.

The Company strongly encourages all stockholders to promptly vote.

Important Information

The Company has filed a definitive Proxy Statement with the Securities and Exchange Commission and has furnished to its stockholders a Proxy Statement in connection with the solicitation of proxies for the Annual Meeting. The Company advises its stockholders to read the Proxy Statement relating to the Annual Meeting, as amended and supplemented, including as amended and supplemented by this supplement, because it contains important information.

Except as described in this supplement, none of the items or information presented in the Proxy Statement is affected by this supplement. This supplement does not provide all of the information that is important to your voting decisions at the Annual Meeting. The Proxy Statement contains other important additional information. We encourage you to carefully read this supplement together with the Proxy Statement.