The 28-year-old set up Jamie Vardy for England's second goal in a 2-0 World Cup qualifying win over Lithuania on Sunday, having also started against Germany in a friendly on Wednesday.
He has featured in 27 of Liverpool's 29 Premier League games so far this term.
There is no timescale on Lallana's recovery, but he could potentially miss five games.
Jurgen Klopp's side host Everton in the Merseyside derby on Saturday at 12:30 BST.
Liverpool midfielder Adam Lallana could be out for up to a month after injuring a thigh on England duty.