The incident occurred during the sixth inning of Boston's home game on Sunday when Duran, who was in the middle of an at-bat, turned toward a heckler whom he told to "shut up" before using a derogatory term for gay men.
Duran, who has since apologised for the incident, will start the unpaid suspension beginning with Boston's game later on Monday against the visiting Texas Rangers.
In his statement of apology, which was released on Sunday by the Red Sox, Duran acknowledged using what he described as a "truly horrific word" when responding to a spectator.
"I feel awful knowing how many people I offended and disappointed. I apologize to the entire Red Sox organization, but more importantly to the entire LGBTQ community," Duran said in the statement.
"Our young fans are supposed to be able to look up to me as a role model, but tonight I fell far short of that responsibility. I will use this opportunity to educate myself and my teammates and to grow as a person."
Duran, who was named the most valuable player of MLB's All-Star Game in July, is in the midst of a breakout season with the Red Sox as he has a .291 batting average along with 14 home runs and 29 stolen bases.