Exhibit 5.1

June 16, 2023

Aptose Biosciences Inc.

251 Consumers Road, Suite 1105
Toronto, Ontario, M2J 4R3

Dear Sir/Mesdames:

We have acted as Canadian counsel to Aptose Biosciences Inc. (the “Company”) in connection with the preparation and filing with the United States Securities and Exchange Commission (the “Commission”) under the United States Securities Act of 1933, as amended (the “Securities Act”), of the Company’s Registration Statement on Form S-1 dated June 16, 2023 (the “Registration Statement”), relating to the resale from time to time by Keystone Capital Partners, LLC (the “Selling Shareholder”) of up to an aggregate of 1,257,785 common shares of the Company (the “Common Shares”) pursuant to a common share purchase agreement entered into between the Company and the Selling Shareholder dated as of May 25, 2023 (the “Purchase Agreement”), which includes (i) 1,232,629 Common Shares that the Company may sell to the Selling Shareholder, from time to time, at the Company’s sole discretion, pursuant to the Purchase Agreement (the “Placement Shares”), (ii) 7,547 Common Shares issued to the Selling Shareholder on May 25, 2023 as consideration for its commitment to purchase Common Shares under the Purchase Agreement (the “Initial Commitment Shares”), and (iii) 17,609 Common Shares to be issued to the Selling Shareholder as consideration for its commitment to purchase Common Shares under the Purchase Agreement (the “Back End Commitment Shares”).

Scope of Review, Assumptions and Qualifications

As counsel, we have made such investigations and examined the originals, or duplicate, certified, conformed, facsimiled or photostatic copies of such corporate records, agreements, documents and other instruments and have made such other investigations as we have considered necessary or relevant for the purposes of this opinion, including:

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The Purchase Agreement and the Registration Rights Agreement are collectively referred to herein as the “Transaction Documents”.

We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such records of the Company and such agreements, certificates of public officials, certificates of officers, or other representatives of the Company, and such other documents as we have deemed necessary or appropriate as a basis for the opinion set forth herein.

In our examination, we have assumed the legal capacity of all natural persons, the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as certified, conformed, photostatic, electronic, or facsimile copies and the authenticity of the originals of such documents. In making our examination of executed documents or documents which may be executed, we have assumed that the parties thereto, other than the Company, had or will have the power, corporate or other, to enter into and perform all obligations thereunder and have also assumed the due authorization by all requisite action, corporate or other, and execution and delivery by such parties, of such documents and that such documents constitute or will constitute valid and binding obligations of the parties thereto. We have also assumed that the Certificate of Compliance will continue to be accurate as at the date of issuance of any Back End Commitment Shares or Placement Shares.

In connection with our opinions expressed below, we have assumed that, at or prior to the time of the delivery of any such Back End Commitment Shares or Placement Shares, the authorization to issue the Back End Commitment Shares and the Placement Shares pursuant to the Purchase Agreement will not have been modified or rescinded by the Board of Directors of the Company and there will not have occurred any change in law affecting the validity or enforceability of such issuance of Back End Commitment Shares or Placement Shares. We have also assumed that neither the issuance and delivery of the Back End Commitment Shares or Placement Shares, nor the compliance by the Company with the terms of the Purchase Agreement, will violate any applicable federal, provincial or state law or will result in a violation of any provision of any instrument or agreement then binding upon the Company or any restriction imposed by any court or governmental body having jurisdiction over the Company.

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, we are of the opinion that:

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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 contained 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