Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We have issued our report dated February 21, 2019, with respect to the consolidated financial statements included in the Annual Report of Moleculin Biotech, Inc. on Form10-K for the year ended December 31, 2018. We consent to the incorporation by reference of said reports in the Registration Statements of Moleculin Biotech, Inc. on Forms S-1 (File No. 333-214898, File No. 333-224243, File No. 333-226146 and File No. 333-227845), Form S-3 (File No. 333-219434) and on Forms S-8 (File No. 333-212619 and File No. 333-225867).

/s/ GRANT THORNTON LLP

Houston, Texas

February 21, 2019