Ramires was injured during the second half of Saturday's tie at Loftus Road and was stretchered from the pitch following a lengthy delay.
The Brazilian is thought to have damaged his medial knee ligament and manager Andre Villas-Boas is confident Ramires will not require an operation.
"It looks like a medial ligament injury, not so bad in terms of knee injuries," said Villas-Boas.
"He will have the MRI scan tomorrow, I think hopefully he will avoid an operation.
"We could look at four weeks (out). We have to see the full extent of the injury."
Fellow midfielder Frank Lampard missed the 1-0 success over QPR, but could return to face Swansea in midweek, although John Obi Mikel remains sidelined.
Villas-Boas added: "Frank we have to see how he comes back for training, he is still a doubt, a 50 per cent chance, and Mikel shouldn't make it."
