Muzzle descends from Old French musel, a diminutive of muse (snout), from Medieval Latin musum (snout, muzzle). The deeper origin of musum is uncertain — it may be of Gaulish or other pre-Latin origin, part of the substrate vocabulary that Latin absorbed from the languages of conquered peoples.
The word entered English in the 15th century with its animal sense: the projecting part of an animal's face including the nose and mouth. The diminutive suffix embedded in the word (Old French musel = little snout) suggests that muzzle was originally applied to smaller animals before being generalized.
The extension to firearms occurred naturally through visual metaphor: the open end of a gun barrel, projecting forward, resembles an animal's snout. This metaphor produced the compound terms that now dominate the word's usage: muzzle velocity (the speed of a projectile as it exits the barrel), muzzle flash (the visible light produced at the barrel's end), muzzle brake (a device that redirects gases to reduce recoil), and muzzle-loader (a firearm loaded through the barrel end).
The verb 'to muzzle' — to put a restraining device on an animal's mouth — extended metaphorically to mean suppressing speech or expression. 'To muzzle the press' or 'to muzzle dissent' draws on the image of an animal forcibly prevented from biting or barking. This figurative usage dates from the 16th century and has become the word's most common verbal sense.
The French cognate museau (snout) has its own culinary significance: museau de porc (pig's snout) is a traditional French charcuterie item — sliced, vinaigrette-dressed pig muzzle served as a cold appetizer. The dish is a reminder that in traditional cuisine, every part of the animal was consumed, including the projecting face parts that gave muzzle its name.
The relationship between muzzle and the verb muse (to ponder) has been debated. Some scholars see a connection through the idea of an animal holding its muzzle still in a posture of contemplation, but this etymology is considered uncertain at best.