Drury was scratched from Friday's Cactus League lineup due to a bruised left hand, Daryl Van Schouwen of the Chicago Sun-Times reports.
It's unclear when Drury suffered the injury, but he'll be held out for at least one spring game. The 32-year-old signed a minor-league deal with the White Sox during the offseason and is expected to be included on the Opening Day roster given his 1.260 OPS during spring training.