Griffin was benched for the contest to allow his sprained knee more time to heal, a decision he said on Twitter Saturday night was out of his hands.
"The decision was not my own. ... But I will be there for my team!!! In every way I possibly can," Griffin wrote.
The Washington Post said Griffin would not play Sunday. If Cousins gets into trouble, veteran Rex Grossman will take over the offense.
The Redskins have won four consecutive games and Griffin's quarterback ranking of 104.7 was tied for the best in the NFL with New England's Tom Brady.