Johann Bayer named this constellation Apis, the Bee, in 1603. However, perhaps because of its similarity with Apus, the Bird of Paradise, its name was changed.
Edmond Halley renamed it Musca Apis, the Fly Bee. Then, Abbé Nicolas Louis de Lacaille named it Musca Australis vel Indica (The Southern or Indian Fly), which distinguished it from the now obsolete Musca Borealis, the Northern Fly. When the Northern Fly was merged with Aries by the International Astronomical Union in 1929, Musca Australis was given its modern, shortened name, Musca.