O'Riordan, 46, was found dead in a London hotel on Monday morning during a recording trip to London ahead of a planned tour, her publicist said. No cause of death has been given.
London police said in a statement that a 46-year-old woman was discovered at a hotel in London's Park Lane early on Monday and was pronounced dead at the scene. "The death is not being treated as suspicious," the statement said.
O'Riordan was catapulted to fame as a shy 22-year-old in 1993 when songs from her debut album were picked up by MTV. The band, whose hits included "Linger" and "Zombie" went on to sell over 40 million records to become Ireland's second-best-selling rock band after U2.
After she pleaded guilty to headbutting and spitting at an Irish police officer in 2014, she told an interviewer that she had been diagnosed with bipolar disorder and was struggling with the breakdown of her marriage.
Ireland's Prime Minister joined a chorus of praise for O'Riordan's work, describing her as the "voice of her generation." U2 said in a tweet that they were "floored" by the news of her death.