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.
Meanwhile, Liverpool captain Steven Gerrard is back in training after being rested at the weekend.
Gerrard was left out of the squad for Sunday's home defeat to West Brom as a precaution in order to protect a minor hamstring niggle.
With nothing but pride left to play for in the Premier League, manager Kenny Dalglish does not want to take any chances with the England international with an FA Cup final coming up in just over a week's time.
"He's fine, no problem," was the Scot's assessment on Gerrard.
"We said it was just a precaution so he's back training. He's been training all week, so there's no other problems."