Brunson, who suffered the injury during Saturday's loss to Atlanta, will travel on the team's upcoming four-game road trip while rehabbing.
"He will travel and begin rehabbing and we'll see where we are then," Carlisle said. "We've got J.J. [Barea], who is always ready. He'll be in the middle of it. He's a great luxury to have sitting there."
Brunson is averaging 8.2 points, 2.4 rebounds and 3.3 assists in 17.9 minutes per game in 57 appearances this season.
The Associated Press contributed to this report.