Exhibit 8.1

April 2, 2015

Ladies and Gentlemen:

We have acted as United States counsel to Aptose Biosciences Inc., a corporation existing under the Canadian Business Corporations Act (the “Company”), in connection with the preparation of a prospectus supplement dated April 2, 2015 (the “Prospectus Supplement”) to the Company’s base prospectus dated December 24, 2014 (the “Base Prospectus” and, together with the Prospectus Supplement, the “Prospectus”) in the form filed by the Company with the United States Securities and Exchange Commission (the “Commission”) pursuant to Rule 424(b) of the rules and regulations promulgated under the Securities Act of 1933, as amended (the “Securities Act”). We understand that the Base Prospectus forms part of the Company’s registration statement on Form F-3 (File No. 333-200660) initially filed on December 1, 2014 with the Commission under the Securities Act, and the general rules and regulations promulgated thereunder (such registration statement, as supplemented or amended at the date of the Sales Agreement (as defined below), including all documents filed as part thereof or incorporated by reference therein, is referred to as the “Registration Statement”).

We understand that the Prospectus is being filed in connection with the establishment of an “at-the-market” offering (the “Offering”) facility under which the Company may, from time to time, issue and sell common shares (the “Shares”), no par value, of the Company having an aggregate offering price of up to US$20,000,000 pursuant to the sales agreement dated April 2, 2015 between the Company and Cowen and Company, LLC, as sales agent.

You have requested our opinion concerning the statements in the Prospectus Supplement under the heading “Material United States Federal Income Tax Considerations” in connection with the Offering.

Our opinion is based upon the existing provisions of the Internal Revenue Code of 1986, as amended, Treasury Department regulations issued thereunder, published administrative positions of the Internal Revenue Service (the “IRS”) contained in revenue rulings, revenue procedures and other administrative pronouncements and judicial decisions, all as in effect as of the date hereof and all of which are subject to change, which may be retroactive, and to differing interpretations. Any change in these authorities could affect the opinion set forth herein. Nevertheless, we undertake no responsibility to advise or notify you of any developments in the application or interpretation of these authorities that occur after the date of our opinion. Our opinion is not binding on the IRS or the courts. Accordingly, there is no assurance that the IRS will not assert a contrary position or that a court will not agree with such a contrary position.

Aptose Biosciences

April 2, 2015

Page 2

For purposes of rendering this opinion, we have reviewed and relied on the Prospectus Supplement and such other agreements, instruments and documents as we have deemed necessary or appropriate, and we have reviewed such questions of law as may be considered necessary or appropriate. In rendering this opinion we have also relied on factual representations and determinations made by the Company as set forth in a Tax Representation Certificate delivered to us on or before the date hereof. Our opinion is also based on the assumption that the Offering will be consummated as described in the Prospectus Supplement, and that there are no arrangements, understandings, or agreements among any persons other than those described in the Prospectus Supplement.

In rendering our opinion, we have assumed the authenticity of all documents submitted to us as originals, the genuineness of all signatures thereon, the legal capacity of natural persons executing those documents and the conformity to authentic original documents of all documents submitted to us as copies. We have assumed that all factual representations and determinations on which our opinion is based are true and correct as of the date given and thereafter where relevant (without regard to whether such representations or determinations are made “to the best knowledge of” any person or party or with similar qualification) and that no actions have been or will be taken which are inconsistent with such representations or determinations.

Based upon and subject to the foregoing, we are of the opinion that under current U.S. federal income tax law, although the discussion set forth in the Prospectus Supplement under the heading “Material United States Federal Income Tax Considerations” does not purport to summarize all possible U.S. federal income tax considerations of the acquisition, ownership and disposition of Shares to U.S. Holders (as defined therein), such discussion constitutes, in all material respects, a fair and accurate summary of the U.S. federal income tax consequences of the acquisition, ownership and disposition of the Shares to U.S. Holders who purchase the Shares pursuant to the Prospectus Supplement, and represents our opinion as to those matters, subject to the qualifications set forth in such discussion.

Our opinion is limited to the U.S. federal income tax matters expressly addressed herein. No opinion is expressed and none should be inferred as to any other matter.

We hereby consent to the filing of this opinion with the Commission as an exhibit to a Report of Foreign Private Issuer on Form 6-K, which will be incorporated by Reference into the Registration Statement. We also consent to the reference to our firm under the heading “Legal Matters” in the Prospectus Supplement. In giving such consents, 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 of the Commission 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.