O'Riordan died in London, where she was recording, publicist Lindsey Holmes said.
"No further details are available at this time," Holmes said, adding that the singer's family was "devastated" by the news.
Formed in Limerick, Ireland at the end of the 1980s, The Cranberries became international stars in the 90s with hits including "Zombie" and "Linger" that fused the alternative rock edge with Celtic-infused pop tunefulness.
Irish President Michael D. Higgins said O'Riordan and the band "had an immense influence on rock and pop music in Ireland and internationally."
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O'Riordan was The Cranberries' chief lyricist and co- songwriter, and her powerful, sometimes wailing, voice was key to the band's distinctive sound.
The group's 1993 debut album "Everybody Else Is Doing It, So Why Can't We?" sold millions of copies and produced the hit single "Linger."
The follow-up, "No Need to Argue," sold in even greater numbers and contained "Zombie," a howl against Northern Ireland's violent Troubles that topped singles charts in several countries.
The members of The Cranberries reunited that year, releasing the album "Roses" in 2012.
The Cranberries released the acoustic album "Something Else" in 2017 and had been due to tour Europe and North America. The tour was cut short because O'Riordan was suffering from back problems.
In 2014, O'Riordan was accused of assaulting three police officers and a flight attendant during a flight from New York to Ireland. She pleaded guilty and was fined 6,000 euros (USD 6,600).
O'Riordan is survived by her ex-husband, the former Duran Duran tour manager Don Burton, and their three children.
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