Henderson scored in the 3-1 win against Brighton on Wednesday before limping off late on in the match.
Klopp said the England international should be fit again for the delayed start to the 2020-21 season.
But Henderson, 30, who has been a key part of this season's Premier League-winning side will not need surgery.
"It's not cool but it's the best we could get," Klopp said on Friday.
"Hendo is an animal, he fights with everything. So he can really deal well with pain. At this moment he knew something had happened. It was a complete mood killer.
"Everybody felt for him. He deserves to lift the trophy and he will lift the trophy.
"There's no surgery needed, that's the good news and all the rest we can make our own decisions, but Hendo will lift the trophy."