56-year-old Sinéad O'Connor died.
Her relatives said "with great sadness" that "her family and friends are devastated". Death was unspecified.
Her 1990 number-one hit Nothing Compares 2 U made her famous worldwide.
Taoiseach (Irish PM) Leo Varadkar said her music "was loved around the world and her talent was unmatched".
Irish President Michael D. Higgins lauded O'Connor's "authenticity" and "beautiful, unique voice".
"What Ireland has lost at such a relatively young age is one of our greatest and most gifted composers, songwriters, and performers of recent decades,
one who had a unique talent and extraordinary connection with her audience, all of whom held such love and warmth for her," he said.
The singer, born Sinead Marie Bernadette O'Connor in Glenageary, County Dublin, in December 1966, had a tough childhood.
She spent her teens at Dublin's An Grianan Training Centre, one of the Magdalene laundries that imprisoned immoral girls.
O'Connor's musical career began when a nun gave her a guitar and a music teacher.
The Lion And The Cobra, her 1987 debut, reached the UK and US top 40.
I Do Not Want What I Haven't Got followed, including Nothing Compares 2 U.
After singing Bob Marley's War a cappella, she glanced at the camera and shouted "fight the real enemy" to protest Catholic Church child sexual assault.