The Reds midfielder was forced off the pitch during Liverpool's Club World Cup final triumph against Flamengo on Saturday evening.
Oxlade-Chamberlain appeared to land awkwardly after a challenge and was in visible pain as Liverpool's medical staff assessed him.
The 26-year-old was seen after the game holding crutches and wearing a protective boot around his ankle, although Klopp was hopeful the injury wasn't "too serious."
Speaking to reporters ahead of Liverpool's visit of Leicester City on Boxing Day, the Reds boss confirmed Oxlade-Chamberlain will be out of action until at least the new year.
"With Oxlade, yeah, it is what we probably expected," Klopp said.
"We have three ligaments on the outside of the ankle and one of them is damaged.
"We have to see how quickly we can fix that. I had that injury myself but it was years ago.
"It can take a while, or it can be quicker, we have to see. He has no chance, of course, for Thursday, no chance.
"This year, Oxlade will not play anymore, that's clear.
"We have to see how quickly it can settle."
"Both, and Fabinho are in a really good way, but, of course, not ready for these games," Klopp added.
Liverpool could go thirteen points above second-placed Leicester City, with a game in hand, should they come out on top against Brendan Rodgers' side on Thursday.