Horford suffered the injury Thursday during the second half of Atlanta's double-overtime win over Cleveland.
"We will work with Al and complete our due diligence to determine the next best steps for him," General Manager Danny Ferry said in a statement. "Injuries are part of the challenge of an NBA season."
Horford has appeared in all of Atlanta's 29 games, averaging 18.6 points and 8.4 rebounds per contest.
The Hawks, with a 16-13 record, are one of just three teams in the Eastern Conference with a winning record.