Cozart's injury flared up during Friday night's 17-inning loss to the Giants, and he was given the day off Saturday. Cincinnati has an off day Monday following its four-game series in San Francisco.
Cozart is expected to be off three days to help alleviate the soreness.
The Reds start a three-game road series against the defending champion Chicago Cubs on Tuesday.
Cozart leads National League shortstops with a .995 OPS and .336 batting average. He snapped an eight-game hitting streak Friday by going 0-for-6 in the 3-2 defeat to the Giants.
Chris Biderman is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.