The band's Twitter account confirmed the news in a post describing Shelley as "one of the UK's most influential and prolific songwriters".
Their singles included "Ever Fallen in Love (With Someone You Shouldn't've)", the explicit "Orgasm Addict" and "What Do I Get?"
Details are scarce on Shelley's passing, but a heart attack is suspected as the official cause of death. It did not elaborate on the details of Shelley's death but said that more information would be released later.
Erlewine wrote Buzzcocks was one of the most influential groups to emerge in the initial wave of punk rock - even lending inspiration to Nirvana.More news: 3 astronauts enter International Space Station
Former Sex Pistols bass player and songwriter Glen Matlock said he was "totally shocked and saddened" by the "untimely death".
Peter Hook, the bassist and co-founder of Joy Division and New Order, tweeted: "Pete Shelley - a true gent! The first album I ever owned was Love Bites by Buzzcocks". He was a fearless iconoclast who wrote songs that could rage and yet be joyful, that could be both positive and cynical, all in a two minute blast of energy that was built to blow your face off. "You'll be missed Pete but you'll be remembered for a long long time for your brilliant music". Buzzcocks formed in 1976 with Shelley and Howard Devoto, who left the band in 1977 to form Magazine.
He tweeted: "Pete Shelley wrote flawless three minute pop songs".
Thorn called Shelley an "amazing songwriter", while Gaiman tweeted, "part of my youth dies with him".