The Scotland midfielder, who has not played since March 21, is also out of contention for a place in the Britain squad for the London 2012 Olympics.
"There is no operation needed but he won't play this season," Dalglish was quoted as saying on Liverpool's website.
"And I would think if they had any designs on having him in the Olympics he wouldn't be fit for that either."
Adam, signed from Blackpool, will also miss Liverpool's final four Premier League matches against Norwich City, Fulham, Chelsea and Swansea City.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.