''For everyone's good it's important that I get it sorted and come back fit and strong in the summer,'' Vaughan told BBC Radio Five Live.
''I didn't want to go through a whole series letting the team and myself down,'' he said.
Vaughan's injury had earlier kept him out of the away series against Pakistan and his withdrawal from the India series has left the English side considerably weak after vice-captain Marcus Trescothick left due to some personal problems.
Andrew Flintoff, who will lead the side in his absence, remains the only player in the team to have played against India.
Vaughan said he withdrew in the larger interest of the team.
''As captain you must be on your game all the time. I don't feel I can play to the best of my ability and help the team as best I can when the knee's causing me problem.'' England rushed Alastair Cook, Owasis Shah and James Anderson to cover for the injured.