The Rockies announced the move before Thursday afternoon's game against the Arizona Diamondbacks.
The team didn't reveal a timetable for his return. Story had an MRI on Thursday and is set to see a hand specialist.
Story suffered the injury during Wednesday's victory over Arizona. He is batting .294 and leads all National League shortstops with 17 home runs (tied with Javier Baez) and 48 RBIs.