Menza collapsed while performing with his current band OHM at the Baked Potato club in Studio City, California, where he lived, said family spokesman J. Marshall Craig, who is also Menza's biographer.
The band had been performing its third song of the first set late on Saturday when Menza collapsed, Craig said. Audience members and friends tried to resuscitate him until medics arrived, but Menza died in an ambulance en route to a local hospital after 25 minutes of resuscitation attempts.
"Despite his excellent health and extremely active, sober lifestyle, a heart attack is his suspected, though not confirmed, cause of death," Craig said. An autopsy will be performed, he said.
Menza was the longest-serving drummer for Megadeth from 1989 to 1998, a period when the band was considered at its height, Craig said. He recorded drums and toured on the albums "Rust in Peace," "Countdown to Extinction," "Youthanasia" and "Cryptic Writings".
Menza was asked by Megadeth co-founder Dave Mustaine to join the band in 1989, after first playing live with the group the year before in Bradford, England, according to Menza's website.
Halfway through a 1998 tour, Menza discovered a tumor on his knee and was forced to leave for surgery. Megadeth hired a replacement and Menza was not asked back, the website said.
In an upcoming memoir, Menza has nothing but praise for his former bandmates, including Mustaine, and considered himself fortunate to have been a part of a legendary band, Craig said.
He had been playing in OHM, which included fellow Megadeth alumnus Chris Poland, for more than one year after various solo stints, Craig said.
Menza was also an accomplished artist and woodworker, and was set to unveil an art series in Houston next month.