Roll up your sleeve and flex your biceps. The Romans, watching the same gesture, thought the swelling under the skin looked like a small animal moving. The Latin word for "muscle" was musculus — literally "little mouse."
From Mus to Musculus
Latin mūs meant "mouse"; the diminutive ending -culus made it "little mouse." Greek had done exactly the same thing centuries earlier: the Greek word for muscle, mŭs, also meant mouse. Two unrelated cultures looked at a moving biceps and reached for the same metaphor.
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Into English
The word came into English in the late 14th century via Old French muscle — itself a borrowing from Latin. Anatomical writing of the time was almost entirely in Latin, so the technical sense came in alongside everyday usage. By the 16th century "muscle" had its modern medical meaning, though writers still occasionally used it for anything that flexed or moved unexpectedly.
Mussels Are Mice Too
The shellfish called a mussel is the same Latin musculus, by a different route. The dark, smooth shape of the closed shell reminded Latin speakers of a mouse, and that branch of the word travelled through Old English to give us the modern shellfish name. So the bivalve on your dinner plate and the bicep in your arm are, etymologically, the same little mouse.