The Chelsea captain was carried off on a stretcher after 39 minutes of the Premier League match against Liverpool at Stamford Bridge, 19 minutes after heading his side in front with his 50th goal for the club.
Terry, who was returning to domestic action after his four-match ban, was in an accidental collision with Liverpool's Luis Suarez and his knee was injured as his leg buckled as he fell just outside his own penalty area.
Chelsea used their Twitter page and official club website to confirm on Monday: "MRI scans on John Terry's right knee thankfully show no significant damage to the cruciate ligaments.
"Chelsea Football Club's medical team will conduct further tests over the next two or three days once the swelling has subsided to determine how long John will be out, but it will be a matter of weeks not months."
Terry missed three Premier League matches and a League Cup tie against Manchester United after the FA found him guilty of racially abusing Queens Park Rangers defender Anton Ferdinand.