The Brazil international lasted just 20 minutes as a second-half substitute in Liverpool's 2-2 draw with Aston Villa at Anfield on Saturday.
Lucas described hearing a "click" in his knee and reportedly left Anfield on crutches.
In a press conference at Melwood on Thursday, Liverpool manager Brendan Rodgers said: "First of all, personally, I am disappointed for Lucas because he's been very, very important for our squad this season.
"It was something that was innocuous really and has put him out for a few months.
"Hopefully he'll get back sooner rather than later. He'd been in good form this season and had worked his way back into the Brazil squad.
"Knowing what he is like, he'll be back sooner rather than later - and he'll do everything in his power to get back.
"In the meantime, that leaves us short of a really good player."
The setback represents further knee trouble for midfielder Lucas, who missed the second half of the 2011-12 season after damaging his cruciate ligament in a League Cup quarter-final against Chelsea.
He also missed three months last season, his first under Rodgers, after suffering a thigh complaint.
With just over a week remaining until the January transfer window closes, Rodgers could now be tempted to bring in a replacement for Lucas, who will hope to be back in time to play his way into contention for the FIFA World Cup held in his home country later this year.
