Sanchez is expected to miss three to four weeks as a result of the injury.
"Anytime with a groin or a hammy or a quad, you always feel a little nervous," manager Aaron Boone told reporters. "We feel like it was on the better end of things."
Sanchez, who has 14 home runs and 41 RBIs but is hitting just .190 this season after going 0-for-4 on Sunday, was hurt when he tried unsuccessfully to beat the throw to first on his double-play grounder in the 10th inning against Tampa Bay Rays.
Kyle Higashioka, the only other catcher on the 40-man roster, was promoted from Triple-A Scranton/Wilkes-Barre.
Higashioka has 20 career big league plate appearances, having been in nine games for the Yankees last season. He was hitless in 18 at-bats, with two walks.
At Scranton/Wilkes-Barre this season, he is hitting .191 with five home runs and 22 RBIs in 51 games.
Last season, Sanchez slugged 33 home runs and drove in 90 runs while hitting .278.
Boone said he's hopeful the time away could help Sanchez return to that kind of offensive form.
"Hopefully this is a positive," Boone said. "Not only allowing him to get physically right, but hopefully it's a little break for him mentally and he can refresh a little bit. Because I know he has been grinding and working really hard, and probably wearing [the season's struggles] mentally, emotionally a little bit.
"I'm confident we'll have a dynamic player the final couple months of the season."
The Yankees also demoted outfielder Clint Frazier and recalled right-hander Giovanny Gallegos from Scranton/Wilkes-Barre.
--Field Level Media