Old English mus "small rodent," also "muscle of the arm," from Proto-Germanic *mus (cf. Old Norse, Old Frisian, Middle Dutch, Danish, Swedish mus, Dutch muis, German Maus "mouse"), from PIE *mus- (cf. Sanskrit mus "mouse, rat," Old Persian mush "mouse," Old Church Slavonic mysu, Latin mus, Lithuanian muse "mouse," Greek mys "mouse, muscle").
Plural form mice (Old English mys) shows effects of i-mutation. Contrasted with man (n.) from 1620s. Meaning "black eye" (or other discolored lump) is from 1842. Computer sense is from 1965, though applied to other things resembling a mouse in shape since 1750, mainly nautical.