The designated hitter, who is a seven-time All-Star and in his 19th major league season, is batting .245 with five home runs and 23 RBIs in 49 games.
In other moves, the Padres placed right-handed starter Michael Wacha (shoulder inflammation) on the 15-day injured list (retroactive to Sunday) and optioned right-hander Domingo Tapia to Triple-A El Paso.
Padres manager Bob Melvin told reporters that the decision to designate Cruz was a "tough one" but the move was made with versatility in mind.
"He's a big impact in the clubhouse. Across the board, throughout the league, the respect that he brings, playing against him from afar, it's fantastic. He comes as advertised -- leadership, all of the above," Melvin said, according to MLB.com.
"I think it's more about versatility here now. We have a couple guys in he and [Matt Carpenter] that basically just DH. We needed to be able to give some guys some days off a little bit more, need a runner off the bench, need to have a little bit more versatility. So unfortunately, we had to make this move today."
Wacha, who missed a start last month with his shoulder injury, is 8-2 with a 2.84 ERA in 15 starts this season, his first in San Diego. Melvin said he's hopeful Wacha will be able to return after the All-Star break.
Left-hander Jose Castillo, right-hander Matt Waldron and infielder Matthew Batten were recalled from El Paso in corresponding moves.
Cruz, 43, signed a one-year contract with the Padres in the offseason.
He has 464 home runs in his career.
Reuters contributed to this report.