Cruz sustained the injury during Sunday's game against the Angels.
For the 31-year-old Cruz, it is his second trip to the DL this season and fifth in the past two years. In 113 games this season, he is hitting. 270 with 28 home runs, 27 doubles and 84 RBI.
In addition, the Rangers also placed pitcher Darren O'Day on the 15-day DL, retroactive to August 25, thanks to right shoulder inflammation.
The 28-year-old righty is 0-1 with a 5.93 earned run average in 13 games for Texas.
To fill the roster spots, Texas recalled outfielder Leonys Martin and purchased the contract of right-handed pitcher Mark Hamburger from Triple-A Round Rock.
Martin signed a five-year deal with the Rangers in early May, and may be able to make his major-league debut with the call-up. The 23-year-old Cuban hit a combined .295 with the club's Single-A, Double-A and Triple-A affiliates in 2011.
Hamburger turned in a combined 8-4 record with a 3.39 ERA in 42 games (four starts) between Double-A Frisco and Round Rock.
Finally, the club released pitcher Ryan Tucker. A 24-year-old native of suburban Los Angeles, Tucker did not record a decision and pitched to a 7.20 ERA in five appearances this year from April 27-May 17.