Eaton was injured in the fourth inning when he caught Ben Zobrist's liner to deep center. Eaton was fully extended when he made the catch and then tumbled to the ground. He got up favoring his left shoulder, and left fielder Melky Cabrera immediately called for the training staff to come out.
"It was enough to take him out," White Sox manager Robin Ventura said. "He knew right away."
Eaton said he has been experiencing soreness in the shoulder since a recent game against Cleveland.
"I've been able to manage it," Eaton said. "Today, when you are running full speed -- I don't care if you have shoulder soreness or not -- it's probably going to hurt when you land on it like I did. We'll be all right."
Rookie Trayce Thompson took Eaton's spot in center and went 2-for-2, including a double and a run scored. His first Major League hit was an infield chopper in the sixth inning.
Robert Falkoff is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.