Both players were injured in Monday night’s 20-12 loss to the Washington Redskins.
Westbrook suffered a right knee strain and Dawkins suffered a neck stinger as the Eagles dropped their second straight game to begin the 2007 season.
Dawkins was down for a few minutes in the fourth quarter after a hit on Washington tight end Todd Yoder before he was helped off by team trainers.
Westbrook was able to play the entire contest.
Coach Andy Reid did not indicate if either would be available for this Sunday's game against the Detroit Lions.
Also missing Wednesday were tackle William Thomas (back spasms), tight end L.J. Smith (groin) and safety Sean Considine (knee).
Cornerback Lito Sheppard, who missed the game against the Redskins with an MCL sprain, continued to sit out. His status is unknown.
2014: The Year in Music [PHOTOS]