Lindstrom is scheduled to have surgery on Friday to repair a tear in the sheath of his left ankle.
"We'll miss him for a while," White Sox manager Robin Ventura said.
The former closer injured his ankle attempting to field an Alcides Escobar bunt in Chicago's 7-6 win against the Royals on Monday night.
The White Sox placed Lindstrom on the 15-day disabled list Tuesday, making him the eighth White Sox player (six current) to spend time on the disabled list this season.
Jackson Alexander is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.