Story, who was the first Red Sox player to win the award this season, compiled 14 RBIs and 10 runs scored to go along with six home runs in the seven games reflected. The Red Sox went 6-1 during those contests while Story batted .360 (9-for-25) with a 1.120 OPS.
Five of his home runs came as Boston swept its four-game series against the Seattle Mariners, including a three-homer performance Thursday.
Story previously won the National League Player of the Week four times as a member of the Colorado Rockies.
Story and the Red Sox will return to action Tuesday as Boston gets set to open a three-game series in Chicago against the White Sox. Boston, winners of five straight, has won nine of its last 12 games entering the series.