Agger has suffered an injury-plagued season, starting just 16 Premier League games and making three appearances in the last two months. He also spent three months on the sidelines before the turn of the year.
And the club have confirmed that England defender Johnson also faces weeks out of action with a hamstring injury.
Liverpool are still awaiting an update on the fitness of captain Steven Gerrard after he was forced to pull out of Saturday's 2-1 reverse at the Hawthorns.
The loss of Agger and Johnson comes as an added blow to the loss of promising full-back Martin Kelly, who had become one of the few bright spots of the season in Kenny Dalglish's resurgent side.
Dalglish told Liverpool's official website: "Daniel has a problem with the tendon behind his knee and won't be involved again this season. He'll be out for a couple of months before he can start training.
"Glen Johnson has a hamstring problem which is usually about three or four weeks and it's the same for Martin Kelly. We will know about Steven at the end of the week. He will be assessed and we'll see what the story is.
"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.