He played 66 minutes of England's 1-0 friendly loss away to Germany last week before a fine display in Sunday's 2-0 World Cup qualifying win at home to Lithuania, when he is reported to have suffered the injury although he did finish the match.
Lallana has played in 27 of Liverpool's 29 Premier League games this season, scoring seven goals, and his absence is likely to be keenly felt as Juergen Klopp's side look to cement a top-four finish during the remainder of the season.
Liverpool are in fourth place on 56 points, four clear of fifth-placed arch-rivals Manchester United, who have two games in hand in the race for Champions League qualification.
Lallana's first game on the sidelines will be Saturday's Merseyside derby at home to Everton.
(Reporting by Toby Davis; Editing by Ken Ferris)