The Holland international suffered the injury in Bayern’s Champions League clash with Juventus on Wednesday.
“I think that he has a serious injury,” said Bayern boss Louis Van Gaal.
“A diagnosis will be given today (Thursday), but if a player tells me it is serious, then I always believe that it is serious.”
Robben will undergo medical tests in an effort to determine the severity of his injury, but it is feared he may have torn his cruciate knee ligament.
The Dutchman joined the German giants from Real Madrid this summer.
