Ramires was injured halfway though the second half as he blocked a shot from Clint Hill and went off on a stretcher.
The 24-year-old Brazilian had an MRI scan on Sunday which confirmed he had suffered a medial ligament injury to his right knee.
"He is expected to be out for three to four weeks," said a club statement.
Saturday's game was won courtesy of Juan Mata's disputed penalty, about which QPR manager Mark Hughes was in no doubt that it was the wrong decision.
Clint Hill was adjudged to have fouled Daniel Sturridge but Hughes thought that the Chelsea striker went down too easily.
"If Mike Dean watches it again he will see that Daniel Sturridge has gone down very easily and unfortunately the referee has given a foul," Hughes told BBC Sport.
"The referee will be disappointed with that decision because no way was it a penalty.
"We worked exceptionally hard, had good shape and good discipline. Unfortunately, the penalty came when we were having our best period in the game in an attacking sense and it really took the wind out of our sails."
Chelsea boss Villas-Boas refused to discuss the penalty incident, pointing out that his side should not have been reduced to nine men in the league game between the pair in October.
"It's very similar to David Luiz and (Heidar) Helguson here and nobody seemed to criticise anything," said Villas-Boas.
"We finished the game for the league here with nine men and (were) maybe treated unfairly. Maybe QPR this time got treated unfairly."
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