The 26-year-old England international, who moved to Anfield from Saints earlier this month, sustained a knock to his lateral collateral ligament during a session at the Reds' Harvard University training base in Boston.
Although no time-frame has been placed on a return to fitness, such injuries can result in a spell of anywhere up to six weeks on the sidelines.
A quirk of the Barclays Premier League fixture list means Liverpool's first match is at home to Southampton on August 17, with Lallana now facing a fitness race to make the Anfield clash.
He has been assessed by Liverpool's medical staff and does not require surgery.
However, the news is clearly a setback for the England international, who will undergo further assessment by the club's medical team in the United States and on his return to Liverpool.
Lallana, a boyhood Everton fan, completed his Â£25million move to Anfield earlier this month, ending manager Brendan Rodgers' pursuit of a player he identified as a primary target for this summer.
Striker Rickie Lambert, Lallana's England team-mate, also made the move from Saints to Liverpool while Croatia defender Dejan Lovren is widely expected to follow the same path.