Adams was injured while running out a double in the fifth inning of the Cardinals' 6-4 victory over Arizona.
Adams is set to undergo an MRI on Wednesday to determine the extent of the injury.
"I felt fine until I got to the base, and it just tightened up as I rounded the base," Adams said to MLB.com. "It's sore. It doesn't feel great. We'll readdress it [Wednesday]."
Mark Reynolds replaced Adams in the game and will likely take over at first base if Adams misses extended time.
"Mark Reynolds is our guy," Cardinals manager Mike Matheny said. "Let's get him out there and let him play. He's certainly played well enough to deserve to be in there."
The Cardinals sent outfielder Jon Jay on a rehab assignment to Class A Peoria and could have his assignment cut short to fill a roster spot. Jay has not played since May 10 after going on the disabled list with wrist tendinitis.
Adams is batting .243 with four homers and 20 RBI this season for the Cardinals (30-16), who have the best record in baseball and own a 4.5 game lead over the Chicago Cubs in the National League Central.
- Scooby Axson