Old English mus "small rodent," also "muscle of the arm," from Proto-Germanic *mus (source also of Old Norse, Old Frisian, Middle Dutch, Danish, Swedish mus, Dutch muis, German Maus "mouse"), from PIE *mus-, the old Indo-European name of the mouse, retained in several language families (source also of 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.
Parturient montes, nascetur ridiculus mus [Horace]