Santana was hurt Monday night in a home-plate collision with Boston's Ryan Kalish.
Santana will have surgery Friday to repair his lateral collateral ligament. The Indians say the recovery time is four to six months and that Santana is expected to be ready for the 2011 season.
The 24-year-old Santana made his major league debut this season. He hit .260 with six home runs and 22 RBIs.
The Indians and Red Sox were finishing their series Thursday at Fenway Park.