Leone was removed from Wednesday's game against the Yankees due to right elbow soreness, Vinnie Duber of AllCHGO.com reports.
Leone was only able to get through one-third of an inning before his elbow forced him out of the game, during which he gave up two earned runs on two hits and two walks. He'll head in for further evaluation Thursday, at which point the White Sox will have a better idea of how long the 32-year-old will be sidelined.