The rookie shortstop, who began the day leading the National League with 27 home runs, initially got hurt Saturday night in the fourth inning on a headfirst slide into second base. He stayed in the game at first, but came out in the bottom half after aggravating the injury when he dove for a ball in the hole.
''It didn't feel good, initially,'' Story said. ''I didn't think it was too serious, but it definitely affected me.
''After the first time, I could handle it, but I kind of re-aggravated it on that dive, and just decided to play it safe.''
X-rays were negative, but Story might have an MRI on Monday after the Rockies return home. He is batting .272 with 72 RBIs.
''We're just looking at a few days here, obviously,'' manager Walt Weiss said.
Cristhian Adames started at shortstop Sunday as the surging Rockies tried for a four-game sweep of the New York Mets. Colorado had won five straight and nine of 10 to reach the .500 mark.
''We're right in the thick of it right now and everybody's banged up and there's a lot of stuff that, people aren't feeling good, and there's just some things that you've got to play through, and that's what I'm planning on doing,'' Story said.
The 23-year-old slugger said his thumb was sore but his goal is to return to the lineup Tuesday night at home against the Los Angeles Dodgers, following the team's off day on Monday.
''Last night it was swollen, but not too bad. Nothing too crazy,'' Story said Sunday. ''Once the swelling goes down - and it already has a little bit - so once that happens then we'll get back into the grip and stuff like that and seeing how it feels.''
In addition, slumping third baseman Nolan Arenado was rested Sunday to give him consecutive days off. Arenado, selected to his second straight All-Star Game this season, was second in the NL in runs (71) and tied for second in homers (26) and RBIs (79).