After limping off during the game and undergoing scans, it was revealed that the 31-year-old damaged cartilage in his knee.
As a result of the injury, Foster is expected to miss West Brom's Premier League matches against Manchester City, Queens Park Rangers and Leicester City.
Head coach Tony Pulis has confirmed that Boaz Myhill will replace Foster in goal and added that 20-year-old Jack Rose has been called up as a substitute.
"It's rotten news for Ben because he's been so consistent," Pulis said. "He kept seven clean sheets in 10 games but we have a very able man to step forward in Boaz, who has performed well when he's come into the team."
Foster will also be unavailable for England's Euro 2016 qualifier against Lithuania at Wembley Stadium on March 27.
He will also miss the Three Lions' friendly against Italy in Turin four days later.
"We've got the international break coming up, which I hope will give our medical team the chance to work on Ben's rehab and we will reassess later," Pulis said.