Exhibit 5.1

McCarthy Tétrault LLP Suite 5300, TD Bank Tower Box 48, 66 Wellington Street West Toronto (Ontario) M5K 1E6
Canada Tel:416-362-1812 Fax:416-868-0673    

June 3, 2024 

Aptose Biosciences Inc.

251 Consumers Road, Suite 1105

Toronto, Ontario, M2J 4R3

Dear Sirs/Mesdames:

We have acted as Canadian counsel to Aptose Biosciences Inc. (the “Company”) in connection with the issuance and sale by the Company of: (i) 1,800,000 common shares of the Company (the “Offered Shares”) at a price of US$1.15 per share; and (ii) 2,055,000 pre-funded warrants (the “Pre-Funded Warrants”) to purchase common shares of the Company (the “Pre-Funded Warrant Shares”) in a direct registered offering pursuant to the terms and subject to the conditions of a securities purchase agreement dated May 30, 2024 (the “Purchase Agreement”) entered into between the Company and an investor (the “Purchaser”), all as described in the Company’s Registration Statement on Form S-3 (File No. 333-267801) (as amended and supplemented through and including the date hereof, the “Registration Statement”) filed by the Company with the Securities and Exchange Commission (the “Commission”) under the United States Securities Act of 1933, as amended (the “Securities Act”).

The Offered Shares, Pre-Funded Warrants and Pre-Funded Warrant Shares are collectively referred to herein as the “Offered Securities”.

Scope of Review, Assumptions and Qualifications

We have examined originals or copies, certified or otherwise identified to our satisfaction, of such documents, records of corporate proceedings, certificates of officers of the Company and of government officials and such other material as we have considered necessary or appropriate for the purposes of this opinion, including, without limitation, the following:

(a) the Registration Statement, including the base prospectus dated October 21, 2022 contained therein;

(b) the prospectus supplement dated as of May 30, 2024 prepared by the Company relating to the issuance of the Offered Securities and supplementing the Registration Statement;

(c) the Purchase Agreement;

(d) the form of Pre-Funded Warrants;

page 2

(e) a certificate of compliance under the Canada Business Corporations Act dated June 3, 2024, with respect to the status of the Company as a corporation thereunder;

(f) a certificate of Fletcher Payne, the Senior Vice President, Chief Financial Officer and Secretary of the Company, as to certain factual matters dated June 3, 2024; and

(g) the articles and bylaws of the Company.

For the purposes of this opinion, we have assumed the genuineness of all signatures on all documents examined by us, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as copies, whether facsimile, electronic, photostatic, certified or otherwise, and the authenticity of the originals of such copies. We have assumed the due authorization, execution and delivery of all documents and instruments by or on behalf of parties other than the Company. We have also assumed that insofar as any obligation under the Purchase Agreement is to be performed in any jurisdiction outside the Province of Ontario, its performance will not be illegal or unenforceable by virtue of the laws of that other jurisdiction, and that the representations and warranties of the Purchaser set forth in the Purchase Agreement are true, correct and accurate, and that the Purchaser has complied with its covenants therein in all material respects.

Whenever our opinion refers to shares, whether issued or to be issued, as being “fully paid and non-assessable”, such opinion indicates that the holder of such shares cannot be required to contribute any further amounts to the Company by virtue of its status as holder of such shares, whether in order to complete payment for the shares, to satisfy claims of creditors or otherwise. No opinion is expressed as to actual receipt by the Company of the consideration for the issuance of such shares or as to the adequacy of any consideration received.

The opinions expressed herein are limited to the federal laws of Canada applicable therein (the “Applicable Law”).

Opinion

Based upon and subject to the foregoing and to the qualifications hereinafter set forth, we are of the opinion that:

(a) the Offered Shares, when issued, sold and delivered in the manner and for the consideration stated in the Purchase Agreement, and upon payment of the consideration provided therein to the Company, will be validly issued as fully paid and non-assessable common shares of the Company; and

(b) the Pre-Funded Warrant Shares, when issued and delivered upon exercise of the Pre-Funded Warrants in accordance with their terms, and upon payment of the exercise price thereof, will be validly issued as fully paid and non-assessable common shares of the Company.

page 3

We hereby consent to the filing of this opinion with the Commission as an exhibit to the Registration Statement. We also consent to the reference to our firm under the heading “Legal Matters” in the prospectus and prospectus supplement included in the Registration Statement. In giving this consent, we do not thereby admit that we are in the category of persons whose consent is required under the Securities Act or the rules and regulations promulgated thereunder. This opinion is expressed as of the date hereof unless otherwise expressly stated, and we disclaim any undertaking to advise you of any subsequent changes of the facts stated or assumed herein or any subsequent changes in Applicable Law.

Yours truly,

/s/ McCarthy Tétrault LLP

McCarthy Tétrault LLP