1530s, "a kind of wrap or scarf for the throat and lower part of the face," agent noun from muffle (v.). Mechanical sense of "any device used to deaden sound" is by 1856; specifically as "automobile exhaust system silencer" it is attested from 1895.
muesli
muezzin
muff
muffin
muffle
muffler
mufti
mug
mugger
mugging
muggins