The Giants star defensive end sat out against the Redskins with pain in his neck from a stinger he suffered against the Jets in a preseason game on Aug. 29.
The Giants also were without tight end Travis Beckum, who was inactive with a hamstring injury.
Tuck came to the stadium with the hopes of giving it a try but the team doctor decided it was best to give it another week.
"Dr. (Russell) Warren did some tests on my neck and he saw some things that he wasn't really excited about so we decided to hold it off and go one more week," Tuck said after the game. "I wanted to play this week. Still not 100 percent, but I wanted to give it a go. The doctor said we rather have you out one week than re-aggravating it and going through all this process and be out for the month."
Tuck reiterated that his neck injury is not structural and just a muscle issue.
"Nowhere near Peyton Manning's or (Mathias) Kiwanuka's or anything like that," Tuck said of the neck injuries the Colts quarterback and Giants linebacker have had. "It is all muscle.
It's going to be pretty hard to hold me out two weeks in a row."
Tuck was injured after he shed a block from a tight end before colliding with Jets lineman Vladimir Ducasse on a play during the third quarter. Tuck's left arm slumped and appeared to go limp as he walked off the field.
Tuck said on Thursday that the injury had not improved enough and he expressed concern at possibly harming it even more by playing against the Redskins. He participated in a limited practice on Friday.
"I am concerned but I am not panicked," Tuck said on Thursday. "It is getting better, but just not as fast as I want it to.
"We are going to do what's best," Tuck added. "You don't want to go out there and lose a season off of one game. But if I'm ready to play I will definitely strap it up."
Reserve Dave Tollefson started for Tuck.
Ohm Youngmisuk covers the Giants for ESPNNewYork.com.