The Texan-born 26-year-old, one of the mainstays of the United States squad which will face England at this year's World Cup finals, left the field midway through the second half and his manager Roy Hodgson fears it could be a serious injury.
"The initial prognosis for Clint is not good," Hodgson told the BBC. "It looks he has suffered cruciate knee ligament damage which if he has keeps him out of action for a while.
"We won't know for certain until the scan is completed on Monday but the doctors are normally very good at diagnosing these things and that was their prognosis."
Dempsey, who has scored seven goals this season, is the latest injury blow to Fulham who are already without Bobby Zamora with a collarbone injury.
"It's a concern, especially up front," said Hodgson. "We think that Clint Dempsey, as an all round player, is very useful for us."
(Reporting by Martyn Herman; editing by Pritha Sarkar)