White suffered the injury while participating in basketball activities away from the club.
He'll be re-evaluated after the four-month timeline.
White will likely be sidelined until just over a week before the 2021-22 campaign is reportedly set to tip off on Oct. 19. He'd potentially miss the start of training camps, which are reportedly scheduled to open on Sept. 28.
The 21-year-old started 54 of 69 games for Chicago in 2020-21, playing 31.2 minutes per contest. He averaged 15.1 points, 4.8 assists, and 4.1 rebounds while shooting 35.9% from deep as the Bulls finished 11th in the Eastern Conference.