Exhibit 5.1

Gordon Feinblatt LLC

Attorneys at Law

233 East Redwood Street

Baltimore, Maryland 21202-3332

410-576-4000

www.gfrlaw.com

May 12, 2017

Farmers and Merchants Bancshares, Inc.

4510 Beckleysville Road, Suite H

Hampstead, Maryland 21074

Ladies and Gentlemen:

We have acted as counsel to Farmers and Merchants Bancshares, Inc., a Maryland corporation (the “Company”), in connection with its filing of a Registration Statement on Form S-1, including the prospectus contained therein (the “Registration Statement”), filed on the date hereof with the Securities and Exchange Commission (the “SEC”) under the Securities Act of 1933, as amended, and the rules and regulations promulgated thereunder. The Registration Statement relates to the offer and sale, from time to time, of up to 150,000 shares of the common stock, par value $.01 per share, of the Corporation (the “Shares”) under the Company’s Dividend Reinvestment Plan (the “Plan”).

We have examined copies of (i) the Articles of Incorporation of the Company, (ii) the Amended and Restated Bylaws of the Company, (iii) the Registration Statement and (vi) the resolutions adopted by the Board of Directors of the Company relating to the Registration Statement. We have also examined the Registration Statement and Exhibits thereto (collectively, with the documents described in the preceding sentence, referred to as the “Documents”).

In expressing the opinion set forth below, we have assumed, and so far as is known to us there are no facts inconsistent therewith, that all Documents submitted to us as originals are authentic, all Documents submitted to us as certified or photostatic copies conform to the original documents, all signatures on all such Documents are genuine, all public records reviewed or relied upon by us or on our behalf are true and complete, and all statements and information contained in the Documents are true and complete.

Based on the foregoing, and subject to the qualifications set forth herein, it is our opinion that Shares issued under the Plan, upon the Company’s receipt of the consideration required to be paid therefor, will be duly and validly issued, fully paid and nonassessable.

We are opining only as to the matters expressly set forth herein, and no opinion should be inferred as to any other matter. The foregoing opinion is limited to the laws of the State of Maryland, the applicable provisions of the Maryland Constitution, and reported judicial decisions interpreting these laws, and we do not express any opinion herein concerning any other law. The foregoing opinion is based upon currently existing statutes, rules, regulations and judicial decisions, and we disclaim any obligation to advise you of any change in any of these sources of law or subsequent legal or factual developments which might affect any matters or opinion set forth herein.

We hereby consent to the filing of this opinion letter as an exhibit to the Registration Statement and to the use of the name of our firm therein. In issuing this opinion letter, we do not admit that we are within the category of persons whose consent is required by Section 7 of the Securities Act.

Very truly yours,

/s/ Gordon Feinblatt LLC