Garcia was hurt Monday night while running out a grounder in the second inning of a 10-4 victory over Seattle. He attempted to pull up a few steps short of first base and then fell. He was assisted off the field and left the game.
White Sox manager Rick Renteria says the injury is considered "mild to moderate" and will be reassessed in a few days.
Garcia was an All-Star a year ago but is off to a sluggish start, hitting .233 with one homer and four RBIs in 18 games.
To take his roster spot, the White Sox called up outfielder Daniel Palka from Triple-A Charlotte. He's hitting .286 with seven RBIs in 17 games.