Bagley sustained the injury in Monday's loss to the Portland Trailblazers.
The fifth-year big man is averaging a career-low 10.6 points and 5.9 rebounds while shooting 53.7% from the field in his first full season in Detroit.
The No. 2 overall pick in the 2018 NBA draft has been plagued by injuries in his career.
Bagley missed the first 13 games of the season because of a sprained MCL and bone bruise in his right knee he sustained in the preseason. In early December, he moved into a bench role as rookie Jalen Duren took over the starting spot. He also missed time in his rookie season with knee injuries and fractured his thumb the following season.
Since being traded to Detroit by the Sacramento Kings at the deadline last season, Bagley has appeared in 43 games for the Pistons. He signed a three-year, $37.5 million deal this offseason with Detroit.
The Pistons are already without second-year guard Cade Cunningham, who had season-ending surgery last month for a stress fracture in his shin.
The Pistons are 10-30 and last in the Eastern Conference, one of three teams with 14% lottery odds to land the No. 1 pick in the 2023 draft presumed to be French center Victor Wembanyama.