Story was struck on the hand while swinging at a pitch from Tampa Bay's Corey Kluber in Tuesday's game. His IL stint is retroactive to Thursday, and he'll be eligible to return July 23 against Toronto for Boston's second game after the All-Star break.
Catcher Connor Wong was recalled from Triple-A Worcester to take Story's roster spot before a game at Yankee Stadium.
Story said Saturday afternoon that his hand was improving, and manager Alex Cora said Story planned to test his hand by taking batting practice about 90 minutes before first pitch against the AL East-leading Yankees.
Boston announced that Story was going on the IL about an hour later. He was not in the original starting lineup, although there had been hope he'd play Sunday.
Story, 29, is in the first season of a $140 million, six-year deal with the Red Sox. The former Rockies slugger is hitting .221 with 15 home runs, 58 RBIs and a .713 OPS after leaving hitter-friendly Coors Field. The batting average and OPS would both be career lows, but his defense at second base has been highly regarded after he switched positions in deference to Boston shortstop Xander Bogaerts.