The former England defender had to be stretchered off after Liverpool striker Luis Suarez landed awkwardly on him during the 1-1 draw at Stamford Bridge. But scans revealed the damage was not as bad as feared.
"With JT, we're looking at approximately three weeks," Di Matteo said. "Fortunately, it's not as bad as we first thought. It's an MCL (medial cruciate ligament) strain."
Chelsea visit Di Matteo's former club West Bromwich Albion in the Premier League on Saturday.
As well as the trip to The Hawthorns, Terry is likely to miss the forthcoming league games against Manchester City, Fulham and West Ham United.
A three-week period of unavailability would also prevent him from playing a part in Chelsea's remaining Champions League Group E fixtures, including Tuesday's crucial match at Juventus.
He risks missing out on Chelsea's participation in the Club World Cup in Japan as well, with the London club expected to leave for the tournament on December 9.