Santana was taken off the field with his leg in a cast in the bottom of the seventh inning after being hit by Boston rookie Ryan Kalish, who was trying to score on a play, the Indians said on their website (cleveland.indians.mlb.com).
Dominican Republic-born Santana immediately fell to the ground in pain where he stayed for more than 10 minutes as trainers, coaches and players came to his aid.
The highly regarded 24-year-old catcher was called up to the Major Leagues in June and is batting .260 with six home runs this year.
Chris Gimenez replaced Santana for the remainder of the game.
(Reporting by Jahmal Corner in Los Angeles; Editing by Patrick Johnston)