The 28-year-old played the full 90 minutes as England beat Lithuania 2-0 on Sunday.
But the attacking midfielder was absent from training earlier today with his Liverpool team-mates.
Liverpool stars train with youth players ahead of Merseyside derby
Tue, March 28, 2017
Liverpool's first team stars are joined in training by several members of the youth team as Jurgen Klopp's side prepare for the Merseyside derby against Everton on Saturday (12.30pm)
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First team stars and youth players trained together at Melwood on Tuesday
And it is understood Lallana will be out for up to a month with the injury.
It means Jurgen Klopp will be without one of his most improved players this season for Saturday's Merseyside derby with Everton.
Liverpool midfielder Adam Lallana
Lallana is also likely to miss games against Bournemouth, Stoke City, West Brom and Crystal Palace.
But he could be back for Liverpool's visit to Watford on May 1.