Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

Farmers and Merchants Bancshares, Inc.

Hampstead, Maryland

We hereby consent to the inclusion in this Pre-Effective Amendment No. 1 to the Registration Statement on Form S-1 of Farmers and Merchants Bancshares, Inc. of our report dated February 28, 2017, except for Note 2 to the consolidated financial statements, as to which the date is April 6, 2017, relating to the consolidated balance sheets of Farmers and Merchants Bancshares, Inc. and Subsidiaries as of December 31, 2016 and 2015, and the related consolidated statements of income, comprehensive income, changes in stockholders’ equity, and cash flows for each of the years in the two-year period ended December 31, 2016, which are also included in this Registration Statement.

We also consent to the reference to us under the caption “Experts” in the prospectus that is contained in this Registration Statement.

/s/ Rowles & Company LLP

Baltimore, Maryland

May 24, 2017