As Tilson made the catch, he tangled with Jimenez, who fell to the ground near the left-center field wall.
After being examined, Jimenez walked off the field holding his right arm.
The White Sox said Jimenez left the game because of right elbow soreness and that he would undergo further examination.
Mondesi left the game in the fifth inning after diving on the warning track in a failed attempt to catch a pop foul by Yolmer Sanchez.
Mondesi was led off the field with head trainer Nick Kenney holding his left arm. No additional information was immediately available.