The 24-year-old sustained a knee injury in the Blues' win over Everton last Saturday and he has been unable to fully recover in time for the game at Loftus Road.
"Ramires was 50% negative," said Villas-Boas. "He is out of the game. So let's hope for the Everton game he manages it. If not, he should be okay for Arsenal."
Chelsea go into the match against their London neighbours in third place in the Premier League table, while Rangers currently sit in 11th.