Foster was forced off 12 minutes from full time with an ankle injury during the Baggies' goalless draw at Everton in the Barclays Premier League.
The 32-year-old had otherwise been in superb form, producing a number of fine saves to preserve a clean sheet in front of watching England manager Roy Hodgson.
Clarke said: "In his own words, he felt a pop in his ankle. He said the pain was obviously strong. Ben is not the type of guy to go down if there is nothing wrong.
"The fact he went off the pitch tells you it is an injury we have to be a little bit worried about. At the moment until it is diagnosed we will let the medical people do their job and have a look at the scans.
"It is difficult to say what the prognosis is or the outcome. It is best to say it is just an injury that worries me."
Everton created the better chances throughout the game but Clarke felt his team deserved a point, their first of the season, for their resilience.
He said: "Ben was excellent as were the rest of our team. Our season started today. Last weekend was disappointing. We were determined to come here and address what we didn't do last week."
Clarke felt preparations for the game had gone well despite the disruption of losing Nicolas Anelka in sad circumstances. Summer signing Anelka has been granted indefinite compassionate leave following the death of his agent.