Coach Andy Reid announced the decisions Saturday.
Eagles trainer Rick Burkholder said Vick is symptom-free, but McCoy has headaches and dizziness.
Vick was injured against Dallas on Nov. 11 and didn't play last week in the Eagles' 31-6 loss to Washington, their sixth straight loss. McCoy was hurt in the fourth quarter against the Redskins.
Rookies Nick Foles and Bryce Brown will start in place of Vick and McCoy. Foles will make his second career start at quarterback, and Brown his first NFL at tailback.
Burkholder said Vick has advanced to phase three of the team's five-phase concussion recovery protocol, which is separate from the NFL-mandated concussion program.
"Every thing's progressing as normal with him," Burkholder said. "He reports no symptoms, no headache, no vision problems, no nauseu, no fatigue. He hasn't reported any symptoms after he did his workout today."
Burkholder said Vick participated in moderate heart-rate exercise on a bike machine Saturday and was symptom-free afterward for the first time.
Burkholder wouldn't speculate whether Vick would be able to play against the Cowboys on Dec. 2.
"I'm encouraged at the way he's doing, but if he plays he plays, if he doesn't he doesn't," Burkholder said. "But he's going to be healthy before he plays."
Burkholder said he plans to move Vick into the fourth phase of the team's rehab program Sunday.
"If he doesn't have any symptoms tonight we'll start doing some throwing if he's doing OK," Burkholder said. "I'll get a couple receivers he can throw to and do a little workout."
Burkholder said Vick hasn't yet passed the separate impact test that compares brain function before and after a concussion. Until he passes that and is cleared by both an independent league-approved neurologist and the Eagles' own concussion specialist, he can't practice or play - even if he is in the fifth and final phase of the Eagles' rehab protocol.
"He's still off in a few areas (on the impact test)," Burkholder said. "That's not alarming to us. It happens. He won't return to football practice until I can get him to do a little better on that impact test."
Monday's game will be the eighth Vick has missed because of injury since he became the Eagles' full-time quarterback early in 2010.
Burkholder said Vick wants to play now.
"These guys are all competitors and that's one of the inherent problems with concussion management - they want to play," Burkholder said. "They know the consequences and everything, but they want to play. We know he's anxious to go out there and play but we have to be careful with these guys."
Burkholder said McCoy, who led the NFL last season with 20 touchdowns, remains in phase one of his recovery. He said McCoy won't be given even light exercises until his symptoms diminish further.
"He still has symptoms today," Burkholder said after the team's Saturday practice. "He has a headache, he has periodic dizziness with exertion If he tries to go up steps too fast or tries to pick up his baby, he gets a little fuzzy. It's not nearly as bad as it was in Washington (after the game) but it's still there.
"He's got some sleep issues, where he sleeps a lot and then he's awake and then he can't get back to sleep, that kind of thing, and one of the things that he complains about is sensitivity to noise. Noise in general is bothering him."
Burkholder said McCoy was given an impact test Saturday and "obviously, that's below baseline as well with his symptoms."
Reid also said wide receiver Jason Avant will miss the game Monday night because of a hamstring injury, and running back Chris Polk is out with a toe injury.