Burress pulled the hamstring in the Giants' win over Baltimore on Nov. 16. He then aggravated the injury in the opening series last Sunday against Arizona, and then sat out the rest of that game.
Giants coach Tom Coughlin said Friday that Burress "is progressing, no doubt. He is getting better."
Domenik Hixon, who is dealing with an ankle injury, will start in Burress' place.
The last time Burress missed a game was Nov. 5, 2006, when he sat out with a back injury. He played in every game for the Super Bowl champion Giants last season despite a persistent ankle injury.
Linebacker Jonathan Goff (hamstring) also will not play against the Redskins, while three players -- running backs Brandon Jacobs (knee) and Ahmad Bradshaw (neck) and defensive tackle Fred Robbins (shoulder) -- are listed as questionable. Coughlin said Jacobs was able to practice Friday, while Bradshaw and Robbins could not.