Bregman suffered the injury in the first inning of the Astros' 8-4 win over the Texas Rangers on Wednesday night. He was injured while running to first base when he grounded into a double play.
The 27-year-old Bregman pulled up a few steps before the bag and limped off the field before heading to the clubhouse.
Astros manager Dusty Baker told reporters there currently isn't a timetable for Bregman's return.
"We really don't know," Baker said. "He's being evaluated by doctors today. Even when they do tell us, to tell you how long it's going to be, it's merely a guess. Hopefully he caught it before he got too injured."
Bregman, who spent time on the IL late in the 2020 campaign because of a right hamstring strain, has recorded a .275 batting average with seven home runs and 34 RBIs over 59 games this season.
In 618 career MLB games with the Astros, Bregman has a .282 batting average with 112 homers and 376 RBIs.
The Astros recalled catcher Garrett Stubbs from Triple-A Sugar Land in a corresponding roster move.