Shelley co-founded Buzzcocks in 1976 with singer-songwriter Howard Devoto, who later left the band to leave Shelley as its vocalist and songwriter.
Shelley, whose real name was Peter Campbell McNeish, was born in Leigh, England.
The Manchester band are best known for their hit songs Ever Fallen in Love and What Do I Get?
Shelley died Thursday of a suspected heart attack in Estonia, the country where he made his home, band management told the BBC.
"A more detailed statement will follow".
Tributes to the punk icon were swift and included words from Teenage Fanclub's Norman Blake. Like their contemporaries, the Buzzcocks scorned what they considered the pretensions and bloated style of mainstream groups and turned out brief, stripped-down songs, performed at manic speed.
Stiff Little Fingers singer Jake Burns wrote: "Really saddened to hear about the passing of Pete Shelley. You'll be missed Pete but you'll be remembered for a long long time for your brilliant music".
And singer Tracey Thorn, formerly of Everything But The Girl, said Shelley had been an "amazing songwriter".
Buzzcocks then signed to United Artists in 1977, recording a trio of classic albums for the label: 1978's Another Music in a Different Kitchen and Love Bites, and 1979's A Different Kind of Tension. "'But after all life's only death's recompense'".