Ratliff, a four-time Pro Bowler, officially was ruled out while tight end Jason Witten was listed as doubtful Tuesday.
Ratliff has not practiced since suffering a high ankle sprain in an Aug. 25 preseason game against the St. Louis Rams.
Witten underwent a CT scan Tuesday on his lacerated spleen, but the results were not immediately available. If the spleen is completely healed, the seven-time Pro Bowler could be cleared to play against the Giants. Team doctors also could elect to sideline Witten until Week 2 against Seattle. Witten was a limited participant in practice this week but has not been cleared for contact.
Safety Danny McCray, the Cowboys' best special-teams player, also is doubtful because of a neck injury.
Cornerback Mike Jenkins, who missed all of the offseason workouts, training camp and the preseason while rehabilitating from shoulder surgery, is listed as questionable. Jenkins was a limited participant in the Cowboys' last two practices.
Giants wide receiver Hakeem Nicks (foot) is listed as questionable, but he has said he expects to start and play his normal amount of snaps.
Other Giants listed as questionable are linebacker Michael Boley (hamstring), rookie cornerback Jayron Hosley (toe), linebacker Mathias Kiwanuka (groin), running back Da'Rel Scott (knee) and defensive end Adrian Tracy (hamstring).