| Document And Entity Information | Jul. 22, 2024 |
| Document Information [Line Items] | |
| Entity, Registrant Name | Farmers and Merchants Bancshares, Inc. |
| Document, Type | 8-K |
| Document, Period End Date | Jul. 22, 2024 |
| Entity, Incorporation, State or Country Code | MD |
| Entity, File Number | 000-55756 |
| Entity, Tax Identification Number | 81-3605835 |
| Entity, Address, Address Line One | 4510 Lower Beckleysville Road |
| Entity, Address, Address Line Two | Suite H |
| Entity, Address, City or Town | Hampstead |
| Entity, Address, State or Province | MD |
| Entity, Address, Postal Zip Code | 21074 |
| City Area Code | 410 |
| Local Phone Number | 374-1510 |
| Written Communications | false |
| Soliciting Material | false |
| Pre-commencement Tender Offer | false |
| Pre-commencement Issuer Tender Offer | false |
| Entity, Emerging Growth Company | false |
| Amendment Flag | false |
| Entity, Central Index Key | 0001698022 |
