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:

Incannex Healthcare Inc.

(Name of Registrant as Specified In Its Charter)

(Name of Person(s) Filing Proxy Statement, if other than the Registrant)

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 DECEMBER 18, 2025

This supplement, dated December 16, 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 of the Company (the "Annual Meeting"), with the following information.

Expected Adjournment of Annual Meeting

The Company has been advised that Proposal No. 2, relating to the ratification of the appointment of its independent registered accounting firm (the "Auditor Ratification Proposal"), has been classified as a non-routine proposal due solely to an administrative error by the Company's transfer agent. As a result of this classification, if a stockholder's shares are held in "street name" and voting instructions are not provided to the applicable bank, broker, or other nominee, such intermediary currently lacks authority to vote those shares on the Auditor Ratification Proposal.

Upon becoming aware of this transfer agent error, the Company promptly engaged with the transfer agent and other relevant parties to seek reclassification of the proposal so that the Auditor Ratification Proposal would be treated as routine, which would permit brokers, banks, and other nominees to exercise discretionary voting authority for shares held in street name. However, there can be no assurance that the Auditor Ratification Proposal will be reclassified as routine, and even if such reclassification is ultimately achieved, the Company does not expect that it will occur on or prior to the Annual Meeting scheduled for December 18, 2025.

Accordingly, as a direct result of this transfer agent error, the Company expects that the Annual Meeting will likely be adjourned in order to allow additional time to reclassify the proposal and to solicit the requisite votes to obtain a quorum. If your shares are held in "street name," you are strongly encouraged to promptly provide voting instructions to your bank, broker, or other nominee.

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.