Manager Bud Black said an MRI has not been scheduled, but would likely take place Monday or Tuesday if there is one.
Story left the Rockies' game Thursday against the New York Mets in the bottom of the fourth inning with the injury. His IL move is retroactive to Friday.
An All-Star in 2018 and 2019, Story is in the final year of his contract. He had been considered a possible trade candidate this season before becoming one of the most coveted players on the free-agent market. Story is a smooth fielder who has plenty of power (139 career homers) and speed on the basepaths (two seasons with 20 or more stolen bases).
But he is off to a slow start this season, hitting .255 with five home runs and 23 RBIs.
On Sunday against the Arizona Diamondbacks, Story, 28, broke out of a homer funk with the fourth walk-off homer of his career. It's tied for third-most in franchise history with Charlie Blackmon, Jason Giambi and Larry Walker, behind only Dante Bichette, who had five, and Todd Helton, who finished with seven.
That long ball snapped a 17-game homerless streak for Story, the second-longest of his career.
The Associated Press contributed to this report.