The right-hander experienced tightness after throwing a curveball warming up Tuesday night and didn't enter the game against the Angels.
He was undergoing an MRI exam Wednesday. Manager Bob Melvin said Axford had no issues leading up to the injury.
"None, zero," Melvin said. "It was a complete surprise not only to us but to him."
Right-hander Jesse Hahn was recalled from Triple-A Nashville and will provide length out of the bullpen.
Oakland has six players on the disabled list after needing it a club-record 27 times last season. The A's have had at least three players on the DL every day since July 30, 2011, and haven't had fewer than two since ending the 2006 season with one.