Company: IXHL
Filing Date: 2025-12-18
Form Type: DEFA14A
Source: 0001213900-25-123039
Chunk: 0

Company: Incannex Healthcare Inc.
Filing Date: 2025-12-18
Form: DEFA14A
Chunk 0
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<div align='center'>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.)</div>

| Filed by the Registrant                    |     | ☒ |
| Filed by a Party other than the Registrant |     | ☐ |

Check the appropriate box:

| ☐ | Preliminary Proxy Statement                                                     |
| ☐ | Confidential, for Use of the Commission Only (as permitted by Rule 14a-6(e)(2)) |
| ☐ | Definitive Proxy Statement                                                      |
| ☒ | Definitive Additional Materials                                                 |
| ☐ | Soliciting Material Under §240.14a-12                                           |

| 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):

| ☒ | No fee required                                                                                     |
| ☐ | Fee paid previously with preliminary materials                                                      |
| ☐ | Fee computed on table in exhibit required by Item 25(b) per Exchange Act Rules 14a-6(i)(1) and 0-11 |

<div align='center'>SUPPLEMENT TO THE PROXY STATEMENT FOR THE

ANNUAL MEETING OF STOCKHOLDERS OF

INCANNEX HEALTHCARE INC.

TO BE HELD ON JANUARY 15, 2026</div>

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