The playmaker sustained the issue during the Reds’ Audi Cup final with Atletico Madrid in Munich on Wednesday evening.
Lallana is now likely to be sidelined for ‘a couple of months, not weeks’ as he begins a rehabilitation programme with the club’s medical team, according to Klopp.
The manager told Liverpoolfc.com: “This is certainly not news we would have wanted.
“Unfortunately, the damage is such that it will likely mean Adam is out for a couple of months not weeks, so I think we can pretty much rule him out of August and September.
“Beyond that we will monitor and wait and see. He is a boy with a world-class attitude to everything professionally and he has always come back in good time from injury setbacks since I have been here, so we will see.”