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late 14c., "device put over an animal's mouth to stop it from biting, eating, or rooting," from Old French musel "muzzle," also "snout, nose" (12c., Modern French museau), from muse "muzzle," from Gallo-Romance *musa "snout" (cf. Provençal mus, Old Spanish mus, Italian muso), of unknown origin, possibly related to Latin morsus "bite" (but OED finds "serious difficulties" with this). Meaning "projecting part of the head of an animal" is from early 15c. in English; sense of "open end of a firearm" first recorded 1560s.
"to put a muzzle on," early 15c., from muzzle (n.). Figurative use from 1610s. Related: Muzzled; muzzling.
Grain in the East is usually thrashed by the sheaves being spread out on a floor, over which oxen and cattle are driven to and fro, till the grain is trodden out. Moses ordained that the ox was not to be muzzled while thrashing. It was to be allowed to eat both the grain and the straw (Deut. 25:4). (See AGRICULTURE.)