The Athletics placed Alexander on the 15-day injured list Tuesday with left rotator cuff tendinitis.
Alexander has been a valuable member of Oakland's bullpen since he made his season debut in late May, and he's thrown 5.2 scoreless frames while striking out seven batters over his last six appearances. He'll now be held out until at least Sept. 2, and the A's will promote J.T. Ginn from Triple-A Las Vegas to fill the open roster spot.