The Bulgarian made his first start for City in Sunday's Manchester derby, but was carried off on a stretcher after falling awkwardly in the sixth minute.
He will have more scans on Monday but an initial estimate is that he will be out of action until late November.
"I was examined by doctors but to be honest I still can't tell you the exact diagnosis because there'll be another medical check-up on Monday," Bojinov told Topsport.
"However, the doctor's initial forecast is that it'll be at least three months out.
"It wouldn't be a surprise if I have to undergo surgery."
21-year-old Bojinov joined City from Fiorentina just a week before the start of the Premier League season and had impressed as a substitute against West Ham and Derby.
As well as missing a large chunk of the season for City, Bojinov will also be ruled out of Bulgaria's friendly against Wales on Wednesday and their Euro 2008 qualifiers against Holland and Luxembourg next month.