The 31-year-old centre-back injured his knee after Liverpool striker Luis Suarez fell awkwardly on him during the two teams' 1-1 draw at Stamford Bridge on Sunday
After being left out for the club's Champions League clash against Shakhtar Donetsk, the captain put the Blues ahead in the first half against Brendan Rodgers' side before being stretchered off in the 38th minute with suspected cruciate ligmanet damage.
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"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."
The game marked the skipper's first league appearances since serving a four-match ban for racially abusing QPR defender Anton Ferdinand.
Manager Roberto Di Matteo had lamented after the game Terry's withdrawal as a turning point, with the Blues going on to lose their lead and draw 1-1.