O'Riordan's distinctive Irish lilt and yodel helped fuel the Cranberries' rapid rise in the early 1990s with global hits "Linger", "Dreams" and "Zombie." The band went on to sell over 40 million records to become Ireland's second-best-selling rock band after U2.
Her three bandmates said in a tweet that they were devastated at the passing of an "extraordinary talent".
Irish Prime Minister Leo Varadkar in a statement described her as the "voice of her generation".
But a naturally reserved singer, O'Riordan often struggled with fame, leaving her native Ireland for several years to avoid the spotlight. During her separation from her husband in 2014, she was arrested for attacking a police officer.
"Family members are devastated to hear the breaking news and have requested privacy at this very difficult time," the publicist, Lindsey Holmes, said in a statement. O'Riordan is survived by two daughters and a son.
Police in London said a woman in her 40s was pronounced dead early on Monday at a hotel on Park Lane in central London.
A spokesman said police were continuing inquiries into the death, which was being treated as "unexplained". The woman had yet to be formally identified, he said.
Meteoric rise
The Cranberries shot to fame with their 1993 debut album "Everybody Else Is Doing It, So Why Can't We?" after the hit song "Linger" was picked up by MTV. The band's first three albums sold a combined 28 million copies.
O'Riordan left the Cranberries in 2003 and recorded two solo albums, before the band reformed in 2009.
O'Riordan pleaded guilty to headbutting and spitting at an Irish police officer in 2014 following an alleged air rage incident. She later told an interviewer that she had been diagnosed with bipolar disorder and was struggling with the breakdown of her marriage.
British pop band Duran Duran, whose tour manager, Don Burton, was O'Riordan's husband from 1994 until they separated in 2014 and was father to her children, said in a Twitter posting that they were "crushed" by the news.
U2 said they were "floored" by the news in a statement posted on Twitter.
"Out of the West came this storm of a voice—she had such strength of conviction yet she could speak to the fragility in all of us," the band said.