In a corresponding move, the club recalled infielder Thairo Estrada from Triple-A Scranton/Wilkes-Barre.
Yankees manager Aaron Boone said Judge has a "pretty significant" strain, according to Jack Curry of YES Network. Boone added that he doesn't have a definitive timetable for the 26-year-old's return and that the team will re-evaluate his health in two weeks.
"When you've been in this game long enough, adversity is a reality," Boone said, according to Mark Feinsand of MLB.com. "It's going to come in different shapes, sizes, and forms throughout the course of the season and you never really know. You've got to be able to deal with it and roll with it.
"I feel like our club, our organization more than anyone in the game, is capable of dealing with these adversities. I feel like we have, we will, and the expectation doesn't change: We expect to go out and win games."
Judge injured himself on Saturday against the Kansas City Royals, grabbing his side following a swing in the bottom of the sixth.
The two-time All-Star is hitting .288/.404/.521 with five home runs and 11 RBIs for the injured-ravaged Yankees this season.
"I'm looking forward to our guys coming back, no question," Boone said. "But we embrace the opportunity to have guys that can play significant roles for us stepping up and contributing."
Despite the injuries, the Yankees enter Sunday with a 10-10 record and sit second in the AL East.