The England international limped off after 77 minutes of his side's 0-0 draw with Everton on Saturday and will have surgery on his right foot later in the week.
"There's no hiding the fact this is disappointing news as Ben is a key player for us," Clarke told the Premier League club's website (www.wba.co.uk).
"He was excellent on Saturday before his injury forced him off."
West Brom's reserve keepers are Wales international Boaz Myhill and Luke Daniels, who made his first-team debut when coming on for Foster.
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