"Mustache" appears to be from the mid-late 16th century of French, possibly Italian/Spanish origin.
1580s, from French moustache (15c.), from Italian mostaccio, from Medieval Greek moustakion.
Borrowed earlier (1550s) as mostacchi, from the Italian word or its Spanish derivative mostacho. The plural form of this, mustachios, lingers in English.
(Etymonline)
One can reasonably assume that mustaches were commonly worn also before the 16th century as the following source shows:
Jan. 1st, 1535 – Henry VIII
"In Enland Henry VIII brought back the beard and mustache look. Men wore whatever length and style that suited them".
Questions:
What was the common Middle English term for mustache and why was it replaced? Was mustache used in some literary work that made it popular for instance?
Best Answer
The most likely answer to the first question is that one would simply refer to the facial hair above the upper lip as a kind of beard.
An early attestation in OED under "mustachio" from 1551 -- in fact, the earliest attestation of either "mustachio," "mustache," or any variants, explicitly denotes the word this way.
"Beard" is attested as early as circa 825, making it a much earlier term than "mustache."
Using the word "beard" to refer to a mustache didn't disappear either. This citation from 1760 poses an example of such a use, even though the word mustache would have been well-established by the time of its writing.
As to why the word "mustache" made its rise in the 16th century, I can only speculate. I have no reason to believe the word grew out of any particularly notable use, like that of Shakespeare in 1598.
It would be another notch on a very long belt.