"firearm for infantry" (later replaced by the rifle), 1580s, from French mousquette, also the name of a kind of sparrow-hawk, diminutive of mosca "a fly," from Latin musca (see midge). The hawk so called either for its size or because it looks speckled when in flight.
Early firearms often were given names of beasts (compare dragoon, also falcon, a kind of cannon mentioned by Hakluyt), and the equivalent word in Italian was used to mean "an arrow for a crossbow." Wedgwood also compares culverin, a simple early sort of firearm, from French couleuvrine, from couleuvre "grass snake."
French mousquette had been borrowed earlier into Middle English (late 14c.; c. 1200 as a surname) in its literal sense of "sparrow-hawk."