The concert tour was slated to kick off Feb. 28 at Northrop Auditorium in Minneapolis, the Star Tribune in Minneapolis reported Monday.
The singer, 62, has been ordered to rest for six to eight weeks, however, she hopes to reschedule the U.S. dates for late April and May, Billboard.com said.
Plans for her European tour in June and July have not yet been changed.
"I know I have been breaking my neck and bending over backwards trying to get my new 'Backwoods Barbie' CD and world tour together, but I didn't mean to hurt myself doing it," Parton said in a statement issued to Billboard.com. "But hey, you try wagging these puppies around a while and see if you don't have back problems. Seriously though, the doctors said I will be good as new in a few weeks, and I can't wait to get back out there."
Parton's "Backwoods Barbie" CD is still scheduled to drop Feb. 26.