The A's made the move with Reddick before playing the third game of a four-game series against the Indians, who blanked Oakland 1-0 on Tuesday.
Reddick hurt his wrist colliding with the wall in foul territory while chasing a pop on April 7 at Houston. He missed three games, but the injury was not improving and the A's decided to put him on the DL.
The club also recalled first baseman Daric Barton from Triple-A Sacramento. To clear a spot on the 40-man roster, the A's released left-hander Jordan Norberto.
Reddick is batting just .152 third lowest in the AL with one home run and 14 RBIs in 29 games.