Thornton was supposed to pitch in live batting practice but did not take part because of discomfort. There is no timetable on when he might resume throwing again.
"He said he didn't feel right," manager Robin Ventura said. "We have so much time down here it's just safer to slow him down and get him out of drills and make sure he's comfortable with it before he continues on."
Teams reported to spring training earlier than normal this year in order to let players get ready in advance of the World Baseball Classic, which starts next month.
Even though Thornton's injury is not deemed serious, it still provides plenty of worry for the White Sox, who have big plans for their veteran left-handed setup man. If Thornton has to miss any time, fellow left-handers Hector Santiago and Donnie Veal will have to pick up the slack.
Thornton has high hopes for the season after dropping 22 pounds over the winter. Part of his plan for losing the weight was a nutrition program that was supposed to help his body rebound quickly after he pitches.
"You're concerned every time a guy has that," Ventura said of Thornton's elbow discomfort. "I'm not sure what level he's at, but again, the beauty of being down here so early is that you can give him the time off and he can catch up and there's nothing wrong with it."