The penalty was announced Tuesday by MLB senior vice president Joe Garagiola Jr., two days after Dempster hit A-Rod in the second inning at Fenway Park. Garagiola also fined Yankees manager Joe Girardi for arguing with plate umpire Brian O'Nora on Sunday night.
Dempster could still play if he appeals the penalty. Boston has off days Thursday and Monday, allowing him to serve the suspension while getting pushed back only a couple days in the Red Sox rotation.
Dempster threw one pitch behind A-Rod's knees and two more inside in the second inning. Then his 3-0 pitch struck Rodriguez's left elbow pad and ricocheted off his back.
Girardi sprinted onto the field, screaming at plate umpire Brian O'Nora for not ejecting the pitcher. Girardi was tossed as the benches and bullpens emptied, and Rodriguez homered off Dempster to spark a sixth-inning rally that lifted New York to a 9-6 win.
Dempster maintained he was just pitching inside and wasn't trying to hit Rodriguez.
Earlier Tuesday, Girardi insisted it would be "open season" on Rodriguez if MLB failed to suspend Dempster.
"That baseball is a weapon. It's not a tennis ball. ... It's a weapon, and it can do a lot of damage to someone's life," Girardi said before a doubleheader against Toronto. "And that's why I was so upset about it. You can express your opinion and be upset with someone, but you just can't start throwing baseballs at people. I mean, it's scary."
Girardi said his profane rant at O'Nora probably was the angriest he's been on a ballfield.
Rodriguez was suspended for 211 games on Aug. 5 for violating baseball's drug and labor agreements but is playing while he appeals. Red Sox pitcher John Lackey criticized the rules last week for allowing A-Rod to play.
Girardi said if Dempster wasn't punished, it would make Rodriguez "open season for people, and that can't happen. It's not fair. If a player is suspended for throwing at someone, they're going to get their appeal. Are we just going to throw that out, too?"
New York didn't retaliate Sunday. Girardi wouldn't say whether there is a need to respond when the teams next meet, at Yankee Stadium on Sept. 5.
Girardi said "protecting your own" in baseball has gone on for "for a long time. And unfortunately you're part of those situations sometimes, but that's part of the game."
The manager also discussed the matter with his 6-year-old son, Dante.
"Part of pitching is pitching inside, that's all part of it," he recalled saying. "But I don't ever want you to hit anyone on purpose."
After Sunday's game, Rodriguez declined to say whether Dempster should be suspended.
"I'm the wrong guy to be asking about suspensions. Holy mackerel," A-Rod said with a laugh. "I've got an attorney I can recommend."