The linebacker tore his right pectoral muscle against the Titans on Sunday.
Colt McCoy entered the game in the second half as the Redskins snapped a four-game losing streak.
The Redskins actually have a chance to win against the hapless Titans.
The Redskins are 1-5. That's pretty much it.
The Redskins will attempt to snap their three-game skid against the Cardinals.
The Redskins lost again Monday, their seventh straight loss in primetime.
Griffin could be back from his ankle injury by the end of October.
The defending Super Bowl champions pay a visit to Washington on Monday.
Redskins linebacker Keenan Robinson tweeted that he was hit by a drunk driver on his way home from Washington's loss to the New York Giants.
The Redskins have now lost eight straight games against NFC East rivals.