Company: IXHL
Filing Date: 2025-05-16
Form Type: DEFA14A
Source: 0001213900-25-044454
Chunk: 0

Company: Incannex Healthcare Inc.
Filing Date: 2025-05-16
Form: DEFA14A
Chunk 0
---
<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 Pursuant to § 240.14a-12                                    |

<div align='center'>Incannex Healthcare Inc.

(Name of Registrant as Specified In Its Charter)

(Name of Person(s) Filing Proxy Statement if Other
Than the Registrant)</div>

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 14a6(i)(1) and 0-11. |

<div align='center'>EXPLANATORY NOTE</div>

This
proxy statement supplement, dated May 15, 2025, supplements the proxy statement of Incannex Healthcare Inc. (the “Company”),
dated April 28, 2025 (the “Proxy Statement”), made available to stockholders in connection with its meeting of stockholders
(the “Special Meeting”) to be held via live webcast at www.meetnow.global/M7SKRH9 on Tuesday, May 27, 2025 at 12:30 p.m. Eastern
Time. Subsequent to the filing of the Proxy Statement, the Company filed a Current Report on Form 8-K announcing that the Company entered
into letter agreements (the “Letter Agreements”) with holders (the “Warrant Holders”) of the Company’s Series
A warrants to purchase common stock, which were issued in a private placement pursuant to securities purchase agreements (each, a “Securities
Purchase Agreement”). Pursuant to the Letter Agreements, the Warrant Holders agreed to waive certain share reserve provisions contained
in the Securities Purchase Agreements and in exchange