The 26-year-old midfielder moved to Anfield from Southampton earlier this month for £25million and had been expected to make his debut in a friendly against Olympiakos on Sunday in Chicago.
But a Friday statement on the Liverpool website read: “Lallana sustained a knock to his lateral collateral ligament during a session at the Reds' Harvard University training base in Boston.
“Lallana has been assessed by Liverpool's medical staff and does not require surgery.
“No specific timeframe has been placed on a return to fitness, but injuries of this nature can result in a spell of anywhere up to six weeks on the sidelines.
“The England international will undergo further assessment by the club's medical team in the United States and on return to Liverpool.”
Liverpool's opening Premier League game is against Southampton on 17 August but Lallana is clearly a major doubt for the meeting with his old club.
He was excellent for the Saints last season, earning a place in the PFA's Premier League team of the year, and then went to the World Cup with England, coming off the bench against Italy and Uruguay before starting against Costa Rica.
However, he has now picked up an injury in only his fourth training session with Liverpool, after he and the majority of the club's other England World Cup players joined the club's US tour on Monday.
The Reds have important matches against Manchester City and Tottenham in the early weeks of the Premier League season before beginning their Champions League campaign in September.
Watch Liverpool play Olympiakos in the International Champions Cup live on Sky Sports 1 at 11pm on Sunday night.