Rolling Stone magazine said he died in his sleep Tuesday night.
Burr had played in the band Samson before serving as a member of Iron Maiden from 1980-82. He later performed with the bands Trust, Stratus, Gogmagog, Elixir, Desperado, Praying Mantis and Alcatrazz, Rolling Stone said.
After Burr was diagnosed with multiple sclerosis several years ago, his former band Iron Maiden performed charity concerts to help him pay for his medical bills, VH1 said.
"This is terribly sad news," Iron Maiden founder/bassist Steve Harris said on the band's official website. "Clive was a very old friend of all of us. He was a wonderful person and an amazing drummer who made a valuable contribution to Maiden in the early days when we were starting out. This is a sad day for everyone in the band and those around him and our thoughts and condolences are with his partner Mimi and family at this time."
"I first met Clive when he was leaving Samson and joining Iron Maiden," Maiden singer Bruce Dickinson said on the website. "He was a great guy and a man who really lived his life to the full. Even during the darkest days of his MS, Clive never lost his sense of humor or irreverence."