The goalkeeper has missed Albion's last two matches after undergoing minor surgery last week but may now need a second operation in another part of his groin.
The 29-year-old will definitely miss Saturday's trip to Sunderland and Clarke admits he has no idea when Foster will be available again.
Clarke said: "Ben won't be fit this week. We are thinking he's got a similar problem on the other side of the groin now.
"We will get that checked out but he definitely won't be fit for Saturday."
Asked when Foster was likely to return, Clarke said: "I don't know. I'll leave that to my medical staff and we will assess it again after the weekend."
Clarke also confirmed that Youssouf Mulumbu will miss the Stadium of Light clash with a hamstring problem but Gareth McAuley is available again after a similar injury kept him out of the 2-1 win over Chelsea.