The 24-year-old Senegal winger suffered the damage during last week's 3-1 victory over Everton.
Initial reports suggested Mane's injury was a minor one, but on Friday Klopp confirmed that the player would have to go under the knife.
"Sadio Mane needs surgery," Klopp told the media ahead of his side's clash away to Stoke City on Saturday.
"We're not 100% sure when it will happen. It's clear - season over.
After making a £34million move from Southampton at the start of the season, Mane has arguably been the Reds' stand-out player this season, missing only five games to date.
Liverpool have failed to win any of those five matches, drawing three and losing the other two.
Klopp's side are in third place on the table, two points ahead of Manchester City, who has played one less match.
The Reds have suffered injuries to key players in recent weeks, and continue to be without England internationals Adam Lallana and Jordan Henderson.
"Adam Lallana is much better but isn’t yet back training," Klopp added.
"Similar with Jordan Henderson. Daniel Sturridge is training and we will see."