Braden (5-4, 4.14 ERA) suffered the injury during his last outing Thursday night. He went four innings in a 6-1 loss to the Rangers, giving up nine hits and five earned runs.
Geren said he would decide in the next day or so whether to have Greg Smith, who pitched Friday night, take Braden's turn in the rotation or name a spot starter.
Smith could step in for Braden on his normal five days between starts because the A's have an off-day Monday.
Dennis Georgatos is a contributor for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.