The move is retroactive to Saturday for the 39-year-old designated hitter and first baseman.
Cabrera is batting .256 with four homers and 37 RBIs in 102 games in his 20th year in the majors.
The 12-time All-Star and two-time American League MVP has 506 career homers and 3,079 hits.
Detroit manager A.J. Hinch told reporters after Saturday's game, a 12-2 loss to the Kansas City Royals, that the move did not necessarily signal the end of Cabrera's season.
"We do want him to get some more at-bats this year," Hinch said. "We don't know how long it's going to take until the strength is back. That's the biggest issue with a strain. But we're hopeful he's going to be able to get back in the batter's box this year."
In a corresponding transaction, Detroit selected the contract of Triple-A slugger Josh Lester ahead of Sunday's series finale with the visiting Royals.
Lester, 28, has played 723 games over seven seasons in the minors since the Tigers drafted him in the 13th round in 2015. The infielder has not yet made his MLB debut.
Lester is batting .243 with 25 homers, 35 doubles and 82 RBIs in 125 games this season with Toledo.
To make room for him on the 40-man roster, outfielder Austin Meadows was transferred to the 60-day injured list.