He will miss about four weeks of summer workouts but will be ready for preseason camp in August, the school said.
The school didn't disclose what caused the injury or when it happened.
"It was just minor surgery that I needed to get taken care of," Young said. "I'm happy that I was able to get it done now so I can begin healing and getting back into workouts with my teammates as soon as possible."
Young was the Big 12 freshman of the year after passing for 1,155 yards and six touchdowns and rushing for 988 yards and 11 TDs.