O'Riordan, who was 46, died "suddenly" according to the statement, but no details were given on the cause of her death.
The singer was in London for a short recording session, the statement added.
The Cranberries rose to global fame in the mid-1990s with a string of hits, including "Linger," "Zombie" and "Dreams." The group, from Limerick, has sold more than 40 million albums worldwide.In 2007, O'Riordan launched a solo project with her album "Are you Listening?" before reuniting with the group in 2009. She also teamed up with The Smiths' bassist Andy Rourke and DJ Ole Koretsky to provide the vocals for the group D.A.R.K.
In 2017, The Cranberries released "Something Else," an acoustic album featuring some of the band's most popular hits, along with three new recordings.
But they canceled many dates on their 2017 Europe and North America tour, with the band citing O'Riordan's ongoing back problems as the cause.
On Twitter Monday, The Cranberries said that O'Riordan's family members are "devastated" by the news and have requested privacy.