Dunk was already ruled out of the trip to the Hawthorn as the skipper continues his return to fitness from a knee injury sustained at West Ham last December.
Dunk is scheduled to return for Albion's next Premier League match against Crystal Palace but today Graham Potter also ruled out Webster for Saturday's third round clash.
Webster struggled earlier this season with hamstring problem but the former Bristol Rovers man also picked up a calf injury at West Ham.
He featured during Albion's excellent 3-2 win against Everton last time out but Potter continues to manage his minutes and the 26-year-old will not be risked at West Brom.
Dunk and Webster are the two main fitness issues with Danny Welbeck set to feature as striker continues his return to full fitness after hamstring surgery.
Welbeck scored a dramatic late leveller during the 1-1 draw at Chelsea recently but was rested for the win at Everton.
Potter said, “Adam Webster looks like he might miss the game because of a little bit of fatigue.
"Lewis Dunk will miss this one too as he continues his recovery, which is going well.
"We would see this game as a chance for Danny Welbeck to get some minutes. He's gaining time on the pitch after coming back from injury. That will be important for both him and us."
Potter has already fine-tuned his squad this month ahead of Saturday's match.
Jurgen Locadia’s permanent move to German club Bochum was confirmed on Thursday morning, while fellow striker Aaron Connolly has been allowed to join Championship side Middlesbrough on loan for the remainder of the season.
Brighton on Wednesday announced the signing of 18-year-old Poland midfielder Kacper Kozlowski from Pogon Szczecin but he will be unavailable until next campaign having been immediately loaned to Belgian league leaders Royale Union St-Gilloise.
Potter did not rule out further incomings this month, although he does not envisage any big-money arrivals.
“January is difficult for that type of signing anyway,” he said.
“We’ve always had a good idea of how we want to work in the windows. We work ahead. It’s not like we are caught by surprise.
“We have a strategy, we have an idea of what we want to do as a club and we follow that.
“You’ve always got to be on your toes, you’ve always got to be aware of what’s out there but, at the same time, we’ve got an idea that we want to follow through and we’ll do our best with it.
“I’m really happy with the group we’ve got.”