"The initial prognosis for Clint is not good," said Fulham boss Roy Hodgson.
"It looks he has suffered cruciate knee ligament damage which if he has keeps him out of action for a while."
Dempsey has been a key player for Fulham this season playing 25 times and scoring seven goals and before he was injured he hit the crossbar with a spectacular overhead kick.
"We won't know for certain until the scan is completed on Monday but the doctors are pretty good these days and often their initial prognosis proves to be the correct one," added Hodgson.
Have your say on Dempsey's injury Dempsey has played 44 times for the US, who play England in their opening Group C game in the World Cup in South Africa.
Fulham are already without top-scorer Bobby Zamora, who suffered a collarbone injury earlier this month that will leave him out of action for several weeks and defender John Pantsil who has a knee 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. Now, with him and Zamora out it makes us a bit weaker in that area than we'd like to be.
"Where we are strongest for cover is in midfield. We're not quite so strong in attack."
During the Blackburn defeat Fulham also lost defender Paul Konchesky with an ankle injury at half-time.
"Paul has an ankle injury which shouldn't be as long," said Hodgson.
"But Toni Kallio is a cover for Konchesky so we've got cover in that area."
Despite the injury worries Hodgson says he will not panic and go out and buy someone just as cover in the current January transfer window.
"It's a very difficult market at the moment and there are not that many players that are moving around and we'll be limited in terms of what we can spend," said Hodgson.
"I'm reluctant to go and spend money on a player who may not be, in the long term, a player who is going to make us better.
"We'll get Zamora, Dempsey and Pantsil back and maybe we'll have to accept that we'll have to do our best in the meantime with what we've got.
"I'm still fairly confident that the team, even with the injury situation, are capable of holding their own in this division and we must continue building on the good things we do and hopefully we won't be quite so vulnerable at set plays as we have been in the last two matches."
Hodgson was disappointed to see his side defeated with goals from Chris Samba and Ryan Nelson securing Blackburn's victory.
Fulham have now not won in the Premier League since beating Manchester United just under a month ago.
"It was a strange game. We felt aggrieved when they went ahead as I thought we were playing well," said Hodgson.
"The second was a bad goal to concede and that changed the complexion of the game. It looked offside but wasn't given."