Clark exited last Sunday's 31-7 loss to the Atlanta Falcons in the second quarter and was wearing a walking boot on the sideline.
Brody Eldridge, another tight end, left Sunday's game with a hand injury in the first quarter and is also ruled out of the game.
The 32-year-old Clark has 28 receptions for 287 yards and two touchdowns in nine games played this season, while Eldridge has six catches for 33 yards.
In other injury news, running back Joseph Addai was a limited participant in practice with a hamstring injury.
Addai has not appeared in a game since Indianapolis' Week 7, 62-7, blowout loss to the New Orleans Saints.