The European champions announced Terry would be sidelined for "weeks rather than months" following an MRI scan on the injury to his right knee that forced him off during Sunday's game at Stamford Bridge.
However, that could be anywhere up to five or six weeks and the club added in a statement: "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."
Any absence represents a huge blow for the Blues and could hurt them badly in the three competitions in which they most crave success.
Terry will miss next Tuesday's Champions League Group E game at Juventus, which Chelsea must not lose if they are to keep their fate in their own hands.
That is sandwiched by crucial league matches against West Brom and Manchester City, which the Blues will be looking to win to avoid slipping further behind leaders Manchester United.
An absence of more than four weeks would make Terry a major doubt for the Blues' trip to Japan early next month for the Club World Cup, which manager Roberto Di Matteo last week claimed he was desperate to win.
Chelsea have struggled badly at the back in their captain's absence but Petr Cech, who has worn the armband in the absence of Terry and Frank Lampard, was confident losing the defender for another extended spell would not derail their season. He said: "We managed to play games without him and we have players who will have a chance to impress.
"I have confidence. Obviously, it's a pity we will lose him again but we have a large squad and quality defenders to deal with that. It's important to have people who can step up. This is a chance for the others to shine and we are going to deal with his loss for him."
Terry has demonstrated supreme powers of recovery in the past, coming back from minor surgery on the same knee weeks ahead of schedule last season.
Cech added: "He knows what it takes to come back in good shape and as soon as possible. He always heals well."