Exhibit 5.1

David G. Peinsipp

T: +1 415-693-2177

dpeinsipp@cooley.com

March 31, 2026

Kodiak Sciences Inc.

1250 Page Mill Road

Palo Alto, California 94304

Re: Registration Statement on Form S-8

Ladies and Gentlemen:

We have acted as counsel to Kodiak Sciences Inc., a Delaware corporation (the “Company”), in connection with the filing by the Company of a Registration Statement on Form S-8 (the “Registration Statement”) with the Securities and Exchange Commission (the “Commission”) covering the offering of up to 2,470,338 shares (the “Shares”) of the Company’s common stock, par value $0.0001 per share, issuable pursuant to the Company’s 2018 Equity Incentive Plan (the “Plan”).

In connection with this opinion, we have examined and relied upon (a) the Registration Statement and the related prospectus, (b) the Plan, (c) the Company’s certificate of incorporation and bylaws, each as currently in effect, and (d) such other records, documents, opinions, certificates, memoranda, and instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below. We have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to originals of all documents submitted to us as copies, the accuracy, completeness and authenticity of certificates of public officials, and the due authorization, execution and delivery of all documents by all persons other than the Company. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not independently verified such matters.

Our opinion is expressed only with respect to the General Corporation Law of the State of Delaware. We express no opinion to the extent that any other laws are applicable to the subject matter hereof and express no opinion and provide no assurance as to compliance with any federal or state securities law, rule or regulation.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that the Shares, when sold and issued in accordance with the Plan, the Registration Statement and the related prospectus, will be validly issued, fully paid, and nonassessable (except as to shares issued pursuant to deferred payment arrangements, which will be fully paid and nonassessable when such deferred payments are made in full).

This opinion is limited to the matters expressly set forth in this letter, and no opinion has been or should be implied, or may be inferred, beyond the matters expressly stated. This opinion speaks only as to law and facts in effect or existing as of the date hereof, and we have no obligation or responsibility to update or supplement this opinion to reflect any facts or circumstances that may hereafter come to our attention or any changes in law that may hereafter occur.

We consent to the filing of this opinion as an exhibit to the Registration Statement. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act of 1933, as amended, or the rules and regulations of the Commission thereunder.

Sincerely,

Cooley LLP

By: /s/ David G. Peinsipp

David G. Peinsipp