Beasley missed the team's loss to the Philadelphia 76ers on Saturday due to the injury.
An MRI on Monday revealed a Grade 3 injury. He will be reassessed in three weeks, per the team.
Beasley has been a bright spot for Minnesota, averaging 19.6 points, 4.4 rebounds and 2.4 assists. He was suspended for 12 games without pay in late February in the wake of pleading guilty to a felony count of threats of violence as a result of an incident in September.