The goalkeeper limped off during Saturday's 1-0 Barclays Premier League win over Stoke and scans have revealed damaged cartilage.
Foster was expected to be included in the England squad for the Euro 2016 qualifier against Lithuania and friendly with Italy this month but will now miss out.
West Brom boss Tony Pulis said: "It's rotten news for Ben because he's been so consistent.
"He kept seven clean sheets in 10 games but we have a very able man to step forward in Boaz [Myhill], who has performed well when he's come into the team.
"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."