The White Sox placed Thorpe on the 15-day injured list Friday with a right flexor strain.
It's not clear when Thorpe was injured, but he had surrendered a combined 14 runs over his last two starts. Given the nature of the injury, the rookie right-hander could be in store for a lengthy absence. Thorpe has posted a 5.48 ERA and 25:21 K:BB over 44.1 innings in his first nine major-league starts.