Braden left Saturday's game after five innings with shoulder stiffness. He is 1-1 with a 3.00 ERA in three starts this season, a year after pitching a perfect game against the Tampa Bay Rays.
Harden has been out with a strained right shoulder since spring training. He was originally put on the 15-day DL retroactive to March 22.
The A's also announced Monday they acquired left-hander David Purcey from Toronto for minor league right-hander Danny Farquhar.
Farquhar was traded from Toronto to Oakland in November.