"Matip was taken to hospital following the fixture and further assessment deemed an operation is required," the club said in a statement.
"Early indications suggest the centre-back is facing a spell of up to six weeks out of action, though that is dependent on how Matip responds to his treatment and rehabilitation."
Matip could miss at least eight matches, including Premier League games against Manchester United, Arsenal and Manchester City as Liverpool look to hold on to top spot.
With Joe Gomez already out injured, it leaves manager Juergen Klopp with only Virgil van Dijk and Dejan Lovren as senior centre-backs heading into a packed English festive fixture schedule.
(Reporting by Hardik Vyas in Bengaluru; editing by Martyn Herman)
