Smith is listed as probable on the team's official injury report, which was released Friday. Smith previously had said he would attempt to play with the injury, sources told ESPN.
A four-time Pro Bowler, Smith suffered the injury against the New England Patriots on Dec. 16 and has not played since.
Smith likely will need surgery in the offseason, but the veteran defensive end and the 49ers were hoping he would be able to play in the postseason.
Smith's streak of 185 consecutive starts ended when he missed the Dec. 23 loss to the Seahawks. Ricky Jean Francois started the last two regular-season games in place of Smith.
Smith, 33, has 66 tackles and three sacks this season.