Exhibit 23.1

KPMG LLP

100 New Park Place, Suite 1400 Vaughan, ON L4K 0J3

Tel 905-265 5900

Fax 905-265 6390

www.kpmg.ca

Consent of Independent Registered Public Accounting Firm

The Board of Directors

Aptose Biosciences Inc.

We consent to the incorporation by reference in the registration statement (No. 333- 267801) on Form S-3 and the registration statements (No. 333-257446, No. 333- 228794, and No. 333-205158) on Form S-8 of our report dated March 23, 2023, with respect to the consolidated financial statements of Aptose Biosciences Inc. which comprise the consolidated statements of financial position as at December 31, 2022 and December 31, 2021, the related consolidated statements of loss and comprehensive loss, changes in shareholders’ equity and cash flows for each of the years then ended, and the related notes, which report appears in the December 31, 2022 annual report on Form 10-K of Aptose Biosciences Inc. for the fiscal year ended December 31, 2022

/s/ KPMG LLP

Chartered Professional Accountants, Licensed Public Accountants

March 23, 2023

Vaughan, Canada

KPMG LLP, an Ontario limited liability partnership and member firm of the KPMG global organization of independent member firms affiliated with KPMG International Limited, a private English company limited by guarantee. KPMG Canada provides services to KPMG LLP.