Bazemore, tied for second on the team with his average of 12.9 points per game, left Sunday's loss to Chicago in the second quarter after landing awkwardly. He hopped off the court, straight into the tunnel toward the locker room.
The Hawks say that an MRI on Monday revealed the injury.
Backup Jaylen Morris, also injured in the second quarter of Sunday's game, will miss about two to four weeks with a sprained left ankle.
Guard Dennis Schroder, the team's top scorer who missed Sunday's game with a left elbow injury, is listed as probable for Tuesday night's game against Oklahoma City.
The Hawks, tied with Orlando for the worst record in the Eastern Conference, have lost three straight games.