The first of 19 shows had been scheduled for Upper Darby, Pennsylvania, on Friday, but the brothers pulled the plug, spokesman Jesse Derris said on Thursday.
"There is a deep rift within the band," Derris said. "There was a big a disagreement over their music direction."
The national tour was to conclude in Seattle on November 6. Fans who already bought tickets can get refunds from the vendor who sold them, Derris said.
People.com first reported that Nick, 21, Joe, 24, and Kevin, 25, were arguing over the weekend, leading to the cancellation.
The brothers became household names through the Disney Channel "Camp Rock" movie series. They signed with Disney's Hollywood Records label in 2007.
Their albums -- including solo projects -- sold 20 million units worldwide, according to their website.
Nick and Joe released solo albums and pursued acting careers in recent years, while Kevin and his wife, Danielle, have starred in their own reality series, "Married to Jonas," which is in its second season on E!.
Kevin and Danielle, who married in 2009, announced in July that they are expecting their first child together, a girl.
The trio came back together musically earlier this year, releasing singles "Pom Poms" and "First Time." Despite the canceled tour, more tracks are expected from their upcoming fifth studio album.
There is no word on what the disagreement over their musical direction will mean for the planned album.