Smith suffered the injury against the New England Patriots on Dec. 16 and has not practiced since. The four-time Pro Bowler missed this past Sunday against the Seattle Seahawks with what the team listed as an elbow injury.
Smith likely will need surgery in the offseason, but the veteran defensive end and the 49ers are hoping he will be available to play in the postseason, according to sources.
The Niners (10-4-1) can clinch the NFC West title with a win Sunday against the Arizona Cardinals. San Francisco also would secure a bye into the NFC divisional round with a win and a loss by the Green Bay Packers (11-4).
Smith's streak of 185 consecutive starts ended when he missed Sunday's loss to the Seahawks. Ricky Jean Francois started in Smith's place and recorded six tackles.
Smith, 33, has 66 tackles and three sacks this season.