A muon weapon is a type of weapon system, a directed energy weapon which operates by harnessing muon elementary particles.
By the late 2250s, the N'shaii had developed a ship-mounted weapon technology which produced a muon burst and caused severe damage to an enemy starship. When the USS Constitution was first hit by the muon burst in 2257, the Federation had never encountered an alien race who had developed the technology. By 2265, Federation scientists had managed to find a defense against the muon beams. (TOS - My Brother's Keeper novel: Constitution)