Kopech 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.
Reynaldo Lopez replaced Kopech and struck out Garcia. Lopez threw two scoreless innings as the starter on Friday, when the White Sox beat the Rangers 8-3. Johnny Cueto, who was scheduled to start Monday at Detroit, replaced Lopez for the third inning. Cueto allowed a leadoff single to Zach Reks before Eli White homered for a 2-1 Rangers lead.
Kopech (2-2, 1.92 ERA) spoke to the media after the game, saying that he "felt a twinge, pinch or pop or whatever you want to call it. I felt like I couldn't get on it again. We're going to take it day by day, but it's looking like I can be back out there soon."
Chicago manager Tony La Russa agreed, saying Kopech might be able to pitch next Sunday, his scheduled turn in the rotation.
Chicago has seven players on the injured list after placing left-handed reliever Aaron Bummer on the IL before the loss. Bummer, whose move was retroactive to Thursday, has a 3.06 ERA in 20 appearances this season.
The White Sox have lost four of five.
The Associated Press contributed to this report.