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 this Registration Statement on Form F-3 of Aptose Biosciences Inc. of our report dated March 27, 2018, with respect to the consolidated statements of financial position of Aptose Biosciences Inc. as at December 31, 2017 and December 31, 2016, the consolidated statements of loss and comprehensive loss, changes in equity and cash flows for each of the years in the two-year period ended December 31, 2017, and notes, comprising a summary of significant accounting policies and other explanatory information, which report appears in the Annual Report on Form 40-F of Aptose Biosciences Inc. for the year ended December 31, 2017, and to the reference to our firm under the heading “Experts” in the prospectus.

Chartered Professional Accountants, Licensed Public Accountants

April 5, 2018

Vaughan, Canada

KPMG LLP is a Canadian limited liability partnership and a member firm of the KPMG network of independent member firms affiliated with KPMG International Cooperative (“KPMG International”), a Swiss entity. KPMG Canada provides services to KPMG LLP.