1580s, from French moustache (15c.), from Italian mostaccio, from Medieval Greek moustakion, diminutive of Doric mystax (genitive mystakos) "upper lip, mustache," related to mastax "jaws, mouth," literally "that with which one chews," from PIE root *mendh- "to chew" (see mandible).
Borrowed earlier (1550s) as mostacchi, from the Italian word or its Spanish derivative mostacho. The plural form of this, mustachios, lingers in English. Slang shortening stache attested from 1985. Old English had cenep "mustache," which is related to cnafa "boy" (see knave).