The move was announced before the Rangers played their series finale against Detroit on Sunday night.
"Ian went in the cage and when swung, he didn't feel comfortable," Texas manager Ron Washington said. "We didn't want it to get worse, so along with him we decided to put him on the DL."
Because Kinsler entered Friday night's game as a pinch-runner, the DL move was retroactive to Saturday, when Kinsler didn't play. The earliest he would be eligible to return is June 2.
Kinsler is hitting .302 with seven home runs, 20 RBIs and 24 runs scored in 40 games.
Another rookie, Leury Garcia, was in the starting lineup at second base, batting ninth. Shortstop Elvis Andrus was batting in Kinsler's usual leadoff spot. Washington said both Profar and Garcia, who entered Sunday's game batting .241, would play while Kinsler is out.
Both rookies have played shortstop. Washington said one of them could spell Andrus if he needed rest, but "that ain't going to happen right now."
Profar was hitting .278 at Round Rock, where he had an eight-game hitting streak. The 20-year-old Profar made his major league debut last season, hitting .176 in nine games.
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