The 34-year-old suffered the injury in the ninth inning of Monday's win over the Royals attempting to field a bunt. He will return to Chicago to undergo further examination, the team said.
Lindstrom is 2-1 with a 3.32 ERA and six saves in nine opportunities this season for the White Sox (22-24), who will continue their nine-game road trip in Kansas City on Tuesday.
Reliever Javy Guerra has been called up from Triple-A Charlotte to replace Lindstrom on the 25-man roster, but the closer role will likely be by committee until Lindstrom returns, with Scott Downs, Ronald Belisario and Daniel Webb all candidates.
Lindstrom is 17-20 with a 3.55 ERA, 51 saves and 85 holds in eight big league seasons for the Marlins, Astros, Rockies, Orioles, Diamondbacks and White Sox.SI WIRE: MRI for Padres starter Andrew Cashner reveals only ‘soreness and irritation’