The 28-year-old underwent scans on Tuesday which saw him sit out training at Melwood, after suffering the injury in England's 2-0 win over Lithuania on Sunday.
It is the second time this season that Lallana has returned to Anfield injured after representing the Three Lions, although he was only unavailable for two Premier League games then.
The Southampton youth product, who has scored seven goals in 27 league appearances for the Reds during the current campaign, could be absent for up to six top-flight matches this time around.
However, there is a chance that club captain Jordan Henderson could be back for the visit of the Toffees this weekend, but Daniel Sturridge remains absent with a hip problem.