Kopech, who is 2-2 with a 1.94 ERA, was checked on by the training staff with a full count and two outs against Adolis Garcia. He threw a warm-up pitch before spiking the baseball in frustration and walking to the dugout to applause from the fans.
The White Sox provided no immediate word on the injury.
Reynaldo Lopez replaced Kopech and struck out Garcia. Lopez threw two scoreless innings as an opener Friday when the White Sox beat the Rangers 8-3.
Chicago has seven players on the injured list after placing left-handed reliever Aaron Bummer on the IL before Sunday’s game. Bummer, whose move was retroactive to Thursday, has a 3.06 ERA in 20 appearances this season.
The Associated Press contributed to this report.