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

Private and Confidential

Consent of Independent Registered Public Accounting Firm

The Board of Directors Aptose Biosciences Inc.

We, consent to the use of our report dated March 22, 2022, on the consolidated financial statements of Aptose Biosciences Inc., which comprise the consolidated statements of financial position as at December 31, 2021 and December 31, 2020, the related consolidated statements of loss and comprehensive loss, changes in shareholders’ equity and cash flows for each of the years in the two-year period ended December 31, 2021, and the related notes, which are incorporated by reference and to the reference to our firm under the heading “Experts” included in the registration statement (No. 333-[ ]) on Form S- 3 of common shares or warrants or any combination of those securities, either individually or in units, up to an aggregate initial offering price of $200,000,000 dated October 7, 2022 of Aptose Biosciences Inc.

/s/ KPMG LLP

Chartered Professional Accountants, Licensed Public Accountants October 7, 2022

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.

Document classification: KPMG Confidential