Amendment No. 1 to Common Stock Purchase Warrant between Annexon, Inc. and Holder

Exhibit 4.1

ANNEXON, INC.

AMENDMENT NO. 1 TO COMMON STOCK PURCHASE WARRANT

This AMENDMENT NO. 1 TO COMMON STOCK PURCHASE WARRANT, dated as of June [•], 2025 (this “Amendment”), amends that certain COMMON STOCK PURCHASE WARRANT (the “Warrant”), dated as of July 11, 2022, by Annexon, Inc. (the “Company”) for the benefit of the holder thereof or its assigns (“Holder”). The Company and Holder are referred to collectively herein as the “Parties.” Capitalized terms used but not otherwise defined herein shall have the meanings set forth in the Warrant.

WHEREAS, pursuant to and in accordance with Section 5(k) of the Warrant, the Warrant may be amended or modified with the written consent of the Company and the Holder; and

WHEREAS, the Company and the Holder wish to amend the Warrant to, among other things, extend the term of the Warrant, effective as of June 30, 2025.

NOW, THEREFORE, in consideration of the rights and obligations contained herein, and for other good and valuable consideration, the adequacy of which is hereby acknowledged, the Parties agree as follows:

Section 1. Term. The reference to 5:00 p.m. (New York City Time) on June 30, 2025 as the “Termination Date” in the Warrant is hereby amended and replaced with 5:00 p.m. (New York City Time) on June 30, 2026.

Section 2. Cashless Exercise. Effective as of the date of this Amendment, the Warrant may not be exercised, in whole or in part, by means of a “cashless exercise.” Accordingly, Section 2(c) of the Warrant is deleted in its entirety and all references to the ability of the Holder to effectuate a “cashless exercise of the warrant” (including, but not limited to such references in Sections 2(a), 2(d), 3(d) and 5(a) of the Warrant) are hereby deleted and shall be of no further effect.

Section 4. No Other Amendments. Each reference to “this Warrant,” “hereunder,” “hereof” and other similar references set forth in the Warrant and each reference to the Warrant in any other agreement, document or other instrument shall, in each case, refer to the Warrant as modified by this Amendment. Except as and to the extent expressly modified by this Amendment, the Warrant is not otherwise being amended, modified or supplemented and shall remain in full force and effect and is hereby in all respects ratified and confirmed, and the execution, delivery and effectiveness of this Amendment shall not operate as a waiver of any right, power or remedy of any party under the Warrant. This Amendment may be executed in two or more counterparts, and each of such counterparts shall be deemed an original, and all of such counterparts together will constitute one and the same agreement.

(Signature Page Follows)

IN WITNESS WHEREOF, the parties hereto have caused this Amendment to Common Stock Purchase Warrant to be executed as of the date first above indicated.

[Signature Page to Amendment to Common Stock Purchase Warrant]