Proto-Indo-European *mūs- became the word for "mouse" in English and many other languages. In Latin it became mūs "mouse", then mūsculus, literally "little mouse", borrowed into English as muscle. The OED tells us that the word for "mouse" also has the meaning "muscle" in many Indo-European languages, because of the resemblance of a flexing muscle to the movements of a mouse.
Weirdly, mūsculus is also the source of mussel, I guess because of the resemblance of the shellfish to mice in size. The Greek cognate μῦς was used for mice, muscles and mussels - and also "a large kind of whale", bafflingly.
It wasn't just muscles and molluscs that were compared with mice. *mūs- became Sanskrit मुष्क muṣka "testicle". Related to this is Persian مشك mušk "musk", since the musk-bags of deer were thought to resemble testicles. The Persian word was borrowed into Greek then Latin as muscus, which is the source of English musk. Muscus is also the source of the -meg in nutmeg, thru Old French mugue "musk", which was used to refer to a fragrant herb.