Robinson suffered the injury in a practice scrimmage, crumbling to the floor after a drive to the basket.
The Pacers consider Robinson, 23, a key part of the franchise's rebuild and plan a prominent role for him in the post-Paul George era.
Robinson, the 2017 NBA slam dunk contest champion, blossomed for the Pacers a season ago into a significant contributor. He averaged a career-high 6.1 points and 3.6 rebounds in 20 minutes a game. Robinson III shot nearly 40 percent from the 3-point line.
After leaving Michigan following his sophomore season, Robinson was a second-round draft pick who had stops with Minnesota and Philadelphia before landing with the Pacers for the 2015-16 season.