The midfielder moved to Anfield for a £25 million fee after representing England at the World Cup but damaged his lateral collateral ligament on Friday.
Lallana is now expected to be sidelined for "up to six weeks", likely ruling him out of Liverpool's first game of the season against former side Southampton.
"Lallana has been assessed by Liverpool's medical staff and does not require surgery," a club statement read."
"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."