The England international, 29, sustained the injury during Liverpool’s friendly match against Atletico Madrid in Munich on Wednesday.
“This is certainly not news we would have wanted,” manager Jurgen Klopp told the Liverpool website.
“Unfortunately, the damage is such that it will likely mean Adam is out for a couple of months not weeks, so I think we can pretty much rule him out of August and September. Beyond that we will monitor and wait and see.
“He is a boy with a world-class attitude to everything professionally and he has always come back in good time from injury setbacks since I have been here, so we will see.”
Lallana was one of Liverpool’s stand-out performers last season, making 31 league appearances and scoring eight goals as Klopp’s men secured a top-four finish.
He stands to miss Liverpool’s two-legged Champions League play-off against Hoffenheim as well as league games against Watford, Crystal Palace, Arsenal, Manchester City, Burnley and Leicester City.