Reds boss Kenny Dalglish also said the Scotland international would not be fit to be considered for selection for Great Britain's Olympic team for this summer's London Games.
"There is no operation needed but he won't play this season," said Dalglish.
"And I would think if they had any designs on having him in the Olympics he wouldn't be fit for that either."
The midfielder will miss the four remaining games in the Premier League and the FA Cup final against Chelsea.
Adam joined Liverpool from Blackpool for a fee of £9 million last summer and has scored twice in 28 Premier League appearances for the club.