Beginning his professional musical career at the age of 18 drumming in the band Rhodes featuring singer Kelly Rhoads, brother of the late Randy, Nick released his first record with Rhoads called "Into The Future" in Europe. The band hit the road with Foghat for a short time.
Moving on to session playing including styles ranging from R&B to Gospel, Funk and Heavy Metal recording with the likes of John Fogerty, Nick caught the attention of then Megadeth drummer Chuck Behler and became his tech. When Megadeth needed a drummer, Nick Menza was asked by Dave Mustaine to join the band in 1989. Dave noted that Nick previously filled in on drums when Chuck was unable to. This prior experience and personal relationship led to the invitation to join Megadeth for the 1990 recording Rust in Peace (produced by Mike Clink). For the next ten years, Nick became associated with Megadeth's "classic" and most profitable era. With his Greg Voelker Rack System he was known as an impressive showman with trademark drumming. This included a double bass drumset with the Tom-Tom's mounted on a lower chrome rack and all cymbal crashes mounted on a higher rack, which was supported by two chrome bars behind the drummer. This was later adopted by Megadeth in 2004's The System Has Failed, which a similar rack system was used.
Following the reissue of the entire Megadeth catalog, Nick was invited to reunite with Megadeth in Fall 2004 . Days after a reunion was announced Nick was fired after rehearsals and replaced with Megadeth's 4th new drummer who was the brother of Megadeth 5th guitarist. Dave Mustaine said that this was because Nick "just wasn't prepared".
In April 2006 Menza joined the Los Angeles-based metal band Orphaned To Hatred. The group describe their sound as "a continuation of the heavy style of '90s Pantera".