"There was a big disagreement over their music direction," spokesman Jesse Derris confirmed to People.
Over the weekend, an argument between the siblings — Nick, 21, Joe, 24 and 25-year-old Kevin — about the future of the band and its music led to the decision to cancel all 19 shows.
Fans who bought tickets for the tour, which was scheduled to stop in big cities including New York and Seattle, will be refunded.
It's not clear what this news means for the Jonas Brothers, who released their first album, It's About Time, in 2006.
Asked what the future holds, their rep responded, "It remains to be seen".
The trio saw huge success with their 2008 album A Little Bit Longer, which went platinum, and were expected to release a fifth studio album, V, later this year.
Over the past few years, the brothers have each pursued separate projects. Nick and Joe released solo albums and ventured into the world of acting, while Kevin and his wife Danielle — who are expecting their first baby — have starred in their own reality series, Married To Jonas.