Iglesias, who was called up from Triple A Pawtucket on May 24, hit .395 in June, including four doubles, two triples, one home run and six RBIs. He also had an 18-game hitting streak.
Iglesias has played both third base and shortstop. It was the first time a Red Sox rookie has won the award since Jacoby Ellsbury in 2007.
David Lough of the Royals, Nick Franklin of the Mariners, Alex Torres and Wil Myers of the Rays, Oswaldo Arcia of the Twins and Jose Cisnero of the Astros were the other rookies to receive votes for the award.