Smith suffered the injury in a Week 15 win over the New England Patriots and hasn't practiced since. The report states that the injury will likely require surgery in the offseason, but Smith and the 49ers are hoping he can play through the pain.
The 33-year-old Smith, who was voted to his fourth straight Pro Bowl on Wednesday, has 66 tackles and three sacks in 14 games this season.
The 49ers sit first in the NFC West with a 10-4-1 record. They can earn a first-round bye with a win Sunday at home against Arizona coupled with a loss by the Packers in Minnesota.
