Unless he appeals, Dempster's ban will start with Boston's away game on Tuesday in San Francisco. Should he appeal, the suspension will be held in abeyance until the process is complete, MLB said.
The league also handed out an undisclosed fine to Yankees manager Joe Girardi for his role in arguing with plate umpire Brian O'Nora shortly after the Dempster incident.
Dempster threw one pitch behind Rodriguez's knees, followed by two more inside in the top of the second inning of Sunday's game at Fenway Park. His 3-0 pitch struck Rodriguez's left elbow pad before ricocheted off the slugger's back.
Yankees manager Girardi immediately sprinted on to the field yelling at umpire O'Nora for not ejecting Dempster. Girardi was then tossed as the benches and bullpens emptied.
"That baseball is a weapon," Girardi told reporters on Tuesday before New York's doubleheader against the Toronto Blue Jays. "It's not a tennis ball. It's a weapon, and it can do a lot of damage to someone's life.
"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."
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Simon Evans)