The 26-year-old England international, who has just moved to Anfield from Southampton this summer, sustained a knock during a session at the Reds' Harvard University training base in Boston on their USA tour on Friday.
No timeframe has been placed on a return to fitness by the club, but it is expected to mean a spell on the sidelines of anywhere up to six weeks for the attacker.
Through a twist of fate, the Premier League fixture list means that Liverpool's first match is at home to Southampton on August 17, with Lallana now facing a fitness race to make the Anfield clash against his former team-mates.
Liverpool did confirm that their medical staff had assessed the injury and it does not require surgery.