The singer made the announcement Monday in a posting on her website. She wrote that she is "very unwell" and had been advised by her doctor to not hit the road after her "very serious breakdown between December and March."
In December, O'Connor announced her split from therapist Barry Herridge after 16 days of marriage.
The Irish singer-songwriter is best known for the early 1990s hit "Nothing Compares 2 U."
Her latest album -- "How About I Be Me (And You Be You)?" -- was released in February. The 45-year-old says she had planned the tour because of the album's release, but was "attempting to be stronger than I actually am."