The Colts would not say which shoulder was injured.
Addai was hurt on a carry late in the third quarter. Chiefs defensive end Glenn Dorsey tackled Addai, and momentum drove Addai's head and shoulder into the ground.
Addai left the game with 50 yards on 17 carries and five catches for 39 yards. His replacement, Mike Hart, scored a touchdown in the fourth quarter that put the Colts up 19-9.