The move leaves the AL East leaders without one of their steadiest sluggers this season. The 6-foot-3, 225-pound Voit is hitting .280 with 17 homers, 50 RBIs and a .901 OPS.
"Since we've gotten him in the trade last year he's been a great player for us -- period," New York manager Aaron Boone said.
The move is retroactive to Sunday, a day after Voit got hurt. Edwin Encarnacion started at first base Tuesday night in the Subway Series opener against the Mets at Citi Field.
Encarnacion has primarily been used at designated hitter since he was acquired from Seattle. He began the night leading the AL with 24 home runs.
The team thinks Voit can return against Toronto during the weekend right after the All-Star break.
"Even the Sunday game in London, he was out doing his ground balls -- it felt pretty good," Boone said. "But when we did the MRI and there was a low-grade strain in there, just feel like it's something that we don't want him to hurt any worse."
Voit, 28, became the 21st player to go on New York's injured list this season, one more than last year. He is the 14th Yankees player currently on the list, which includes outfielder Giancarlo Stanton and pitchers Luis Severino and Dellin Betances.
First baseman Mike Ford was recalled from Triple-A Scranton/Wilkes-Barre to replace Voit on the roster. Ford has hit .179 with one homer and two RBI across 28 at-bats in the big leagues this season.
Left-hander Nestor Cortes Jr. also was brought up from Triple-A after the Yankees optioned right-hander Chance Adams to their top farm club following Sunday's game.
Designated hitter and first baseman Kendrys Morales was released.
Voit exits with apparent leg injury
Luke Voit goes 4-for-4 on the day with three doubles, but appears to hurt his leg rounding first base and limps into second.