The Super Bowl champion Giants also said Tuesday that defensive tackle Marvin Austin and offensive tackle James Brewer would miss the game with back injuries. Amukamara is out with a sprained ankle suffered in a preseason game on Aug. 24. None of the three practiced this week.
Cowboys starting nose tackle Jay Ratliff (ankle) and rookie safety Matt Johnson (hamstring) were ruled out, while Pro Bowl tight end Jason Witten (spleen) and backup safety Danny McCray are listed as doubtful.
No one on the Giants was listed doubtful.
The Associated Press contributed to this report.