The Dane limped off the pitch during the Reds' defeat by West Brom at the weekend after damaging a tendon.
"Daniel has a problem with the tendon behind his knee and won't be involved again this season," said Reds boss Kenny Dalglish. "He'll be out for a couple of months before he can start training."
Dalglish added that Liverpool defender Glen Johnson also faces three of four weeks on the sidelines after straining a hamstring, while the club's medical staff are yet to complete their latest assessment on Steven Gerrard.
"We will know about Steven at the end of the week. He will be assessed and we'll see what the story is," said the Scot.
"It's disappointing for the players because they want to play in every game. We're getting towards the end of the season but if you're injured you're injured.
"We feel for them but the most important people at the football club are the ones who are fit and able to play. We have to get on with what we've got.
"Fabio Aurelio and Jonjo Shelvey are training again and David Ngog had a game for the reserves on Monday. So we've lost some but we've got a few back."