Dempster was also fined an undisclosed amount, Major League Baseball announced Tuesday.
Dempster hit Rodriguez with a pitch in the second inning of Sunday's game in Boston. His first pitch went behind Rodriguez, two more were inside and the fourth hit Rodriguez.
The incident caused both dugouts to empty.
Game umpires warned Dempster, but didn't eject him. Yankees Manager Joe Girardi argued and was thrown out of the game. Girardi was also fined Tuesday.
The Yankees rallied for a 9-6 win with Rodriguez hitting a home run.
Dempster denied he was trying to hit Rodriguez but was pitching inside to the right-handed hitter.
Rodriguez is playing with the Yankees as he appeals a 211-game suspension handed down recently as part of the baseball's Biogenesis investigation. More than a dozen players have been suspended -- most for 50 games -- after allegedly receiving performance-enhancing drugs from the Biogenesis of America clinic in Florida.
Celebrity Families of 2014 [PHOTOS]