The move was made before Monday night's game at Tampa Bay.
Cruz came out of Saturday night's game with a tight hamstring. An MRI exam on Sunday showed no tear, but inflammation around the muscle.
Cruz had already been on the disabled list twice this season, once for each hamstring. In his 77 games, Cruz is hitting .320 with 16 home runs and 64 RBIs.
Texas also reinstated infielder Joaquin Arias, sidelined since July 31 by a strained back muscle, from the 15-day DL.