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 Post-Effective Amendment No. 1 to the Registration Statement on Form S-1 of Farmers and Merchants Bancshares, Inc. of our report dated February 28 2018 relating to the consolidated balance sheets of Farmers and Merchants Bancshares, Inc. and Subsidiaries as of December 31, 2017 and 2016, 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, 2017, 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

April 18, 2018