The midfielder suffered the injury in the weekend's defeat against Newcastle United.
Sandro signed for the club from Tottenham Hotspur in the summer for around £10 million and has made eight appearances for the club so far.
The Brazilian has had a history of knee injuries, in particular an ACL, but the doctor who is treating him says this particular injury is completely unrelated.
Dr Peter Florida said: “Sandro took a bad knock to his right knee, and has suffered damage to his medial ligaments.
“It is totally unrelated to his previous ACL injury.
“Unfortunately, he will now be unavailable for selection until after Christmas.”
It represents something of a blow for Harry Redknapp and his side with QPR's performances seemingly improving over the past few weeks, with Sandro at the heart of the midfield making himself a bit of a nuisance for the opposition.
The club will hope they have enough depth and experience in the squad over the busy December period to cope with the Brazilian's loss as they look to avoid relegation in their first season back in the Premier League.
They currently sit bottom of the table with eight points, three points from safety.