The Broncos promoted linebacker Shaquil Barrett from their practice squad to take his place.
Smith injured his surgically repaired left knee at practice Thursday and missed Friday's practice. He was the only Broncos player to miss a workout following the team's first-round bye.
Smith played in all but one game for the Broncos this season, totaling 11 tackles and two pass breakups.
Barrett is a rookie from Colorado State who spent all season on the practice squad except for Week 7, when he was on the active roster.
The Broncos (12-4) host the Colts (12-5) Sunday.