In a statement, the band said that doctors had advised Jagger not to tour because he needs to receive medical treatment.
The 17-concert tour was due to kick off in Miami on 20 April, before travelling across North America until a finale in Oro-Medonte, Canada on 29 June.
Jagger, 75, apologised directly to fans on Instagram and Twitter.
"I really hate letting you down like this," he wrote. "I'm devastated for having to postpone the tour but I will be working very hard to be back on stage as soon as I can."