It is the same knee he damaged last season and the former Dutch international will undergo surgery on Wednesday.
"It's a big blow for us to lose Bolo," manager Rafael Benitez told reporters. "He is a big help to all the players here because he mixes very well."
Liverpool play Portsmouth at Anfield in the Premier League on Wednesday with only one recognised central midfielder in Steven Gerrard. Defenders Jamie Carragher or Daniel Agger are likely to play alongside him in midfield.
Gerrard scored his first Premier League goal of the season on Saturday in the 1-0 victory over Manchester City and Benitez wants his skipper to be more greedy.
"He wants to pass the ball and is sometimes too generous to his team mates and we would like to see him hold on to the ball more," said the Spaniard.
Liverpool have agreed a deal to sign Boca Juniors defender Emiliano Insua on loan in January.
The Argentine under-20 international will sign for an 18-month loan period with an option to make the deal permanent.
"He is 17 now but will be 18 when he joins us in January," Benitez said. "He needs time but is a very good player. The question now is how he settles in England and we will see if he can take part in first team games."
