Jones only managed 10 minutes of the 1-1 draw with West Ham at the weekend after coming on as a sub for Chris Samba.
Rovers say the England Under-21 international had undergone "successful" surgery on his injured knee.
Club doctor Phil Batty told the club's official website: "Phil Jones had keyhole surgery to repair the tear to his cartilage. The operation went successfully.
"The rest of the knee looks fine and he'll now begin his rehab which should be three to four months."