Exhibit 1.1

May 15, 2025

Incannex Healthcare Inc.

8 Century Circuit, Suite 105 Norwest

Sydney, NSW 2153, Australia

Attention: Joel Latham

Re: Letter Agreement

Ladies and Gentlemen:

Reference is made to (i) that certain Registration Rights Agreement (the “Registration Rights Agreement”), dated as of March 7, 2025, by and between Incannex Healthcare, Inc. (the “Company”) and the undersigned (the “Investor”), (ii) that certain Securities Purchase Agreement, dated as of March 7, 2025 (the “Purchase Agreement”), by and between the Company and the Investor, entered into in connection with the Company’s private placement pursuant to the Purchase Agreement and other securities purchase agreements with certain institutional investors (collectively, with the Purchase Agreement, the “Purchase Agreements”) pursuant to which the Company sold Common Stock, Pre-Funded Warrants and Series A Warrants for gross proceeds of approximately $12.5 million (the “Private Placement”), (iii) the Series A Warrant issued pursuant to the Purchase Agreement by the Company to the Investor on March 10, 2025 (the “Series A Warrant”), and (iv) that certain at-the-market sales agreement, dated as of April 7, 2025, by and between the Company and A.G.P./Alliance Global Partners, with respect to the offer and sale of Common Stock from time to time (the “ATM Facility”). Capitalized terms used but not defined in this letter shall have the meanings ascribed to them in the Purchase Agreement.

Pursuant to Section 6(b) of the Registration Rights Agreement, the Company may not include any securities of the Company in any Registration Statements other than the Registrable Securities (as defined in the Registration Rights Agreement) (the “Registration Rights Provision”) and is prohibited from filing a Registration Statement (as defined in the Registration Rights Agreement), subject to certain limited exceptions. Pursuant to Section 4.9 of the Purchase Agreement, the Company agreed to reserve and keep available at all times, free of preemptive rights, a sufficient number of shares of Common Stock for the purpose of enabling the Company to issue Shares pursuant to Purchase Agreement and Warrant Shares pursuant to any exercise of the Warrants (the “SPA Reserve Provision”). The Company is subject to the restrictions set forth in Sections 4.12(a) and (b) of the Purchase Agreement (the “Subsequent Equity Sale Restrictions”), subject to certain exceptions set forth in Section 4.12(c) of the Purchase Agreement, including an exception for sales of Common Stock pursuant to the ATM Facility at a price no less than $1.08.

The Investor hereby waives the SPA Share Reserve Provision such that the Company may reserve for issuance under the ATM Facility any of the authorized shares of Common Stock that would otherwise be reserved for issuance under the Investor’s Series A Warrant, with the understanding that (i) the Company may issue sell such shares pursuant to the ATM Facility at any time from and after the date hereof and before the date that the Stockholder Approval is obtained (the “Permitted ATM Sales”), and (ii) following the receipt of the Stockholder Approval with respect to the Authorized Share Increase (as defined in the Series A Warrant), the Company shall reserve the Required Reserve Amount (as defined in the Series A Warrant) after giving effect to any Warrant Cancellation (as defined below).

The Investor hereby waives the Registration Rights Provision and consents to the Company disclosing this letter agreement in its SEC Reports.

The Investor hereby waives the Subsequent Equity Sale Restrictions with respect to any Permitted ATM Sales, whether or not the price is greater than or less than $1.08.

Any aggregate net proceeds to the Company from the Permitted ATM Sales, with such net proceeds being the gross proceeds less the placement agent fee of 3.0% of the gross proceeds to the Company from the Permitted ATM Sales and deal related legal expenses of up to $95,000 (the “Net Proceeds”), up to $12,499,828 in the aggregate during the period commencing on the date hereof and ending the day immediately prior to receipt of the Stockholder Approval, will be paid by the Company to the Investor and the other purchasers in the Private Placement, in accordance with the procedures set forth in the next paragraph, with the Investor receiving its pro rata portion of the Net Proceeds (based on the proportion the Investor’s Subscription Amount bears to the aggregate subscription amount of all purchasers in the Private Placement) received during the period commencing on the date hereof and ending on the earlier of (i) the date the Company raises $12,499,828 in Net Proceeds from the Permitted ATM Sales or (ii) the day immediately prior the Stockholder Approval up to a maximum amount equal to the Investor’s Subscription Amount (the “Warrant Cancellation Payment”). In consideration of the Warrant Cancellation Payment, the original number of Warrant Shares (as defined in the Series A Warrant) as set forth on the first page of the original Series A Warrant, prior to any adjustments as set forth therein, shall be deemed to be reduced by a number of shares (the “Cancelled Warrant Shares”) equal to the quotient obtained by dividing the Warrant Cancellation Payment by $2.14, rounded down to the nearest whole share (the “Warrant Cancellation”). The Warrant Cancellation shall have the same effect as cancellation of the original Series A Warrant and issuance of a new Series A Warrant evidencing the right to purchase the remaining number of Warrant Shares.

On the earlier of (i) the date the Company raises $12,499,828 in Net Proceeds from the Permitted ATM Sales or (ii) the date immediately preceding the date that the Stockholder Approval is expected to be obtained, the Company shall provide a notice setting forth the amount of Net Proceeds, the amount of the Warrant Cancellation Payment and the number of Cancelled Warrant Shares (the “Permitted ATM Sale Notice”) to the Investor at the email address set forth in the Investor’s signature page to the Purchase Agreement. The Warrant Cancellation shall be immediately effective upon the delivery of the Permitted ATM Sale Notice, and the Investor may not exercise the Series A Warrant with respect to any of the Cancelled Warrant Shares. Within three Business Days after the date the Stockholder Approval is obtained, the Company shall pay the Warrant Cancellation Payment to the Investor pursuant to the wire instructions set forth on Exhibit A.

In connection with the foregoing, the Investor represents and warrants to the Company that the Investor (a) is the sole owner of, and has good and lawful title to, the Series A Warrant free of any lien or encumbrance, except for restrictive legends relating to compliance with the Securities Act and (b) has all requisite authority to enter into this agreement and perform its obligations hereunder, including without limitation with respect to any Warrant Cancellation. The Investor further acknowledges and agrees that the Series A Warrant may not be sold, transferred, pledged or assigned unless, in addition to the other procedures set forth in the Series A Warrant, the recipient of the Series A Warrant agrees in writing to be subject all of the terms and conditions of this letter agreement as if it were an original party hereto.

The Company acknowledges and agrees that, except for the waivers, consents and agreements set forth above, the surviving obligations under the Registration Rights Agreement, Series A Warrant and the Purchase Agreement remain unmodified and in full force and effect.

[Signature Pages Follows]

Signature Page to Letter Agreement

Signature Page to Letter Agreement

Exhibit A

Wire Instructions