Exhibit 5.1

August 16, 2018

Carrizo Oil & Gas, Inc.

500 Dallas Street, Suite 2300

Houston, Texas 77002

Ladies and Gentlemen:

In connection with the issuance by Carrizo Oil & Gas, Inc., a Texas corporation (the “Company”), of 9,500,000 shares (the “Shares”) of its common stock, par value $0.01 per share, pursuant to (i) its Registration Statement on Form S-3 (File No. 333-221121) (the “Registration Statement”), which was filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), and (ii) the related prospectus dated October 25, 2017 (the “Base Prospectus”), as supplemented by the prospectus supplement relating to the sale of the Shares dated August 14, 2018 (together with the Base Prospectus, the “Prospectus”), as filed by the Company with the Commission pursuant to Rule 424(b) under the Act, certain legal matters with respect to the Shares are being passed upon for the Company by us. At your request, this opinion is being furnished to you for filing as Exhibit 5.1 to the Company’s Current Report on Form 8-K to be filed with the Commission on the date hereof (the “Form 8-K”).

The opinions set forth herein relate only to certain matters regarding the Shares. In our capacity as your counsel in the connection referred to above, as a basis for the opinions hereinafter expressed, we have examined the Company’s Amended and Restated Articles of Incorporation and Amended and Restated Bylaws, each as amended to date, the Underwriting Agreement dated August 14, 2018 between the Company and Citigroup Global Markets Inc. and Goldman Sachs & Co. LLC, as representatives of the several underwriters named therein, relating to the sale of the Shares (the “Underwriting Agreement”), the originals, or copies certified or otherwise identified, of corporate records of the Company, and certificates of public officials and of representatives of the Company, statutes and other instruments and documents and have made such other investigations as we have deemed relevant and necessary in connection with the opinions hereinafter set forth.

In giving this opinion, we have relied, without independent investigation, on certificates of officers of the Company and of public officials with respect to the accuracy of the factual matters contained in such certificates and we have assumed, without independent investigation, that all signatures on documents we have examined are genuine, all documents submitted to us as originals are authentic, all documents submitted to us as certified or photostatic copies of original documents conform to the original documents and all these original documents are authentic, and all information submitted to us is accurate and complete. We have also assumed that all Shares will be offered and sold in the manner described in the Prospectus and in accordance with the terms of the Underwriting Agreement.

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On the basis of the foregoing, and subject to the assumptions, limitations and qualifications set forth herein, we are of the opinion that the Shares have been duly authorized by all necessary corporate action on the part of the Company and, when issued and delivered against payment of the purchase price therefor in accordance with the Underwriting Agreement will be validly issued, fully paid and nonassessable.

This opinion is limited in all respects to the laws of the State of Texas and the applicable federal laws of the United States.

We hereby consent to the filing of this opinion of counsel as Exhibit 5.1 to the Form 8-K. We also consent to the reference to our firm under the heading “Legal Matters” in the Prospectus. In giving this consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission thereunder.

Very truly yours,

/s/ Baker Botts L.L.P.