Horford underwent an MRI and examination on Friday by Dr. Michael Bernot at Peachtree Orthopaedics in Atlanta that showed a complete tear of the muscle.
"We will work with Al and complete our due diligence to determine the next best steps for him," Hawks president of basketball operations and general manager Danny Ferry said. "Injuries are part of the challenge of an NBA season."
The 27-year-old Horford was hurt in the first overtime when he went for a steal against Cleveland forward-center Anderson Varejao. Horford grabbed his right chest and left the game with a reported shoulder injury.
The Hawks also announced that guard John Jenkins remains out with low back pain.