Exhibit 5.1

1717 Main Street, Suite 3700 Dallas, Texas 75201 +1.214.659.4400 Phone +1.214.659.4401 Fax andrewskurthkenyon.com

December 19, 2017

Independent Bank Group, Inc.

1600 Redbud Boulevard, Suite 400

McKinney, Texas 75069-3257

Independent Bank Group, Inc.

Underwritten Offering of

$30,000,000 5.00% Fixed-to-Floating Rate Subordinated Notes Due December 31, 2027

Ladies and Gentlemen:

Reference is made to: (i) the Underwriting Agreement by and among Independent Bank Group, Inc., a Texas corporation (the “Company”), Independent Bank, a Texas state-chartered bank and wholly owned subsidiary of the Company, and Piper Jaffray & Co. and U.S. Bancorp Investments, Inc., acting individually and as representatives of the several underwriters named in Schedule A thereto (the “Underwriters”), dated December 13, 2017 (the “Underwriting Agreement”); (ii) the Registration Statement on Form S-3 (File No. 333-218782), which was prepared pursuant to the Securities Act of 1933, as amended (the “Securities Act”), and the general rules and regulations of the United States Securities and Exchange Commission (the “Commission”) promulgated thereunder (the “Securities Act Rules”) and was filed with the Commission under the Securities Act and became automatically effective on June 16, 2017 (such Registration Statement on Form S-3, at the time it became effective, the “Registration Statement”); (iii) the Prospectus dated June 16, 2017, constituting a part of the Registration Statement, including the documents incorporated therein by reference at each time pertinent to the offer and sale of the securities described below (the “Base Prospectus”); (iv) the Preliminary Prospectus Supplement dated December 13, 2017, relating to the offer and sale of an unspecified aggregate principal amount of the Company’s 5.00% Fixed-to-Floating Rate Subordinated Notes due December 31, 2027 (the “Notes”), which supplemented the Base Prospectus and which, along with the Base Prospectus, was filed with the Commission pursuant to Rule 424(b)(5) on December 13, 2017 (the “Preliminary Prospectus Supplement”); (v) the Prospectus Supplement dated December 13, 2017, relating to the offer and sale of $30,000,000 in aggregate principal amount of the Notes, which supplements the Base Prospectus and which, along with the Base Prospectus, was filed with the Commission pursuant to Rule 424(b)(5) under the Securities Act on December 14, 2017 (the “Prospectus Supplement”); (vi) the Final Term Sheet dated December 13, 2017, relating to the Notes, which was filed with the Commission on December 13, 2017 pursuant to Rule 433 under the Securities Act (the “Final Term Sheet”) and (vii) the Subordinated Debt Indenture dated as of June 25, 2014 (the “Original Indenture”), between the Company and Wells Fargo Bank, National Association, as trustee under such indenture (in such capacity, the “Trustee”), as supplemented by the First Supplemental Indenture, dated as of July 17, 2014, between the Company and the Trustee and the Second Supplemental Indenture, dated as of December 19, 2017, between the Company and the Trustee (the “Second Supplemental Indenture,” and the Original Indenture as so supplemented, the “Indenture”).

We have acted as special counsel to the Company in connection with the offer and sale of the Notes by the Company.

In rendering this opinion, we have examined and relied upon, without independent investigation or verification, executed originals, counterparts or copies of: the Amended and Restated Certificate of Formation of the Company, and the Third Amended and Restated Bylaws of the Company, each as amended and restated to date and in effect on the date hereof; the Registration Statement; the Base Prospectus; the Preliminary Prospectus Supplement; the Final Term Sheet; the Prospectus Supplement; the Indenture; the global note dated December 19, 2017, which has an aggregate principal amount of $30,000,000, which is issued in the name of Cede & Co., as the nominee of The Depository Trust Company (“DTC”), and which represents the Notes sold to the Underwriters pursuant to the Underwriting Agreement (the “Global Note”); the Underwriting Agreement; resolutions adopted by the Board of Directors of the Company (the

ANDREWS KURTH KENYON LLP

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Independent Bank Group, Inc.

December 19, 2017

Page 2

“Board of Directors”), dated June 16, 2016, and December 7, 2017, and resolutions adopted by the Pricing Committee of the Board of Directors (appointed on December 7, 2017), dated December 13, 2017, relating to the approval of the terms and conditions of, and the Company’s entry into, execution and delivery of, the Original Indenture and the Second Supplemental Indenture, the establishment of the series of the Notes under the Indenture, the establishment of the terms, provisions and conditions of the series of the Notes under the Indenture, and the offer and sale of the Notes pursuant to the Underwriting Agreement (collectively, the “Resolutions”); and such other documents, records and certificates as we considered necessary or appropriate to enable us to express the opinions set forth herein. In all such examinations, we have assumed the authenticity and completeness of all documents and records submitted to us as originals and the conformity to authentic and complete originals of all documents and records submitted to us as photostatic, electronic, conformed, notarized or certified copies.

In rendering this opinion, we have assumed, without independent investigation or the authentication and verification, that: (i) each natural person signing any document reviewed by us had the legal capacity to do so; (ii) each person signing in a representative capacity (other than on behalf of the Company) had the authority to sign in such capacity; (iii) the Underwriting Agreement has been duly authorized and validly executed and delivered by the parties thereto (other than the Company and Independent Bank); and (iv) the Trustee has been at all times from June 16, 2017 through the date hereof eligible to serve as an indenture trustee under the Trust Indenture Act.

As to certain facts material to our opinion, we have made no independent investigation or verification of such facts and have relied, to the extent that we deem such reliance proper, upon a certificate of a public official of the State of Texas, the Company and officers or other representatives of the Company.

Based on the foregoing and subject to the qualifications and limitations set forth below, we are of the opinion that the Notes have been duly authorized and constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms, and are entitled to the benefits of the Indenture.

The foregoing opinion is qualified to the extent that the enforceability of the Indenture, the Global Note, the Notes or any related document or instrument may be limited by or subject to the effects of bankruptcy, insolvency, moratorium, reorganization, liquidation, rearrangement, probate, conservatorship, fraudulent conveyance, fraudulent transfer or other similar laws (including court decisions) now or hereafter in effect relating to or affecting creditors’ rights and remedies generally or providing for the relief of debtors, general principles of equity (regardless of whether such remedies are sought in a proceeding in equity or at law) or public policy.

We note that the enforceability of specific provisions of the Indenture, the Global Note and the Notes may be subject to (i) standards of reasonableness and “good faith” limitations and obligations such as those provided in those provisions of the Texas Business and Commerce Code that are the Uniform Commercial Code as enacted in the State of Texas and similar applicable principles of common law and judicial decisions and (ii) the course of dealings between the parties, the usage of trade and similar provisions of common law and judicial decision.

We express no opinion as to the enforceability of the separability clauses in Section 111 of the Original Indenture and Section 7.04 of the Second Supplemental Indenture or any provision of the Indenture or the Global Note that purports to waive or not give effect to rights to notice, defenses, subrogation or other rights or benefits that cannot be effectively waived under applicable law, including Section 116 and Section 117 of the Original Indenture. We express no opinion with respect to the enforceability of (i) the parenthetical clause in clause (1) of Section 607 of the Original Indenture relating to the limitations on the compensation of trustees or (ii) Section 116 of the Original Indenture or Article 6 of the Second Supplemental Indenture to the extent such provision purports to waive liability for violation of securities laws. We express no opinion as to any provision of the Indenture, the Global Note or the Notes that purports to confer subject matter jurisdiction in respect of bringing suits, enforcement of judgments or otherwise on any federal court, to the extent such court does not otherwise have such jurisdiction.

Independent Bank Group, Inc.

December 19, 2017

Page 3

The foregoing opinions are limited in all respects to matters under and governed by the federal laws of the United States of America and the laws of the State of Texas, in each case, as in force and effect as of the date of this opinion. We do not express any opinion as to the laws of any other jurisdiction.

We consent to the filing by you of this opinion letter as an exhibit to the Company’s Current Report on Form 8-K filed with the Commission on the date hereof and the incorporation by reference of this opinion letter into the Registration Statement, and we further consent to the use of our name under the caption “Legal Matters” in the Preliminary Prospectus Supplement and the Prospectus Supplement. In giving this consent, we do not admit that we are included in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ Andrews Kurth Kenyon LLP

DWM/JAH