Santana was hurt Monday night in a home-plate collision with Boston's Ryan Kalish.
The surgery will be performed to repair the rookie's lateral collateral ligament. The Indians said that the recovery time is four to six months and that Santana is expected to be ready for the 2011 season.
"This is a rare baseball operation," Cleveland trainer Lonnie Soloff said. "It certainly could have been much worse, but we feel that we are fortunate with the limits of the injuries that were sustained. Any surgery on a catcher has to be approached thoughtfully and seriously."
The 24-year-old Santana made his major league debut this season. He hit .260 with six home runs and 22 RBIs.
"The bad part about it is that he is going to lose two months of development and getting to know the pitchers on our staff and the opposition, too," Indians manager Manny Acta said. "The good thing is he is going to get the surgery and be ready for spring training."
The Indians and Red Sox played the finale of their four-game series on Thursday night.