Brazil international Silva was forced off in the first half at the Tottenham Hotspur Stadium after stretching for the ball.
He was replaced by Andreas Christensen, who could now be forced to deputise for the 36-year-old in the centre of defence this weekend.
"It will be very tight for Sunday, only two days recovery," boss Thomas Tuchel said after the match.
"It is too early to give a diagnosis because I saw him very briefly with a big strap around his muscle.
"We will have to wait until Friday so we can confirm it but I think for Sunday he is a big doubt."
Jorginho's 24th-minute penalty sealed the victory for Chelsea and lifted them into sixth spot with 36 points from 22 games.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies