Replays showed Watson running out of bounds and into Kitchings late in the third quarter and Kitchings responding by shoving Watson.
"What occurred on the sideline of the Clemson at NC State game, involving an NC State assistant coach, was inappropriate," the ACC said in a statement. "The matter has been handled by the two schools in a manner that is satisfactory to both schools as well as the conference office; therefore, there will be no further action regarding this matter."
After the game, NC State coach Dave Doeren said Kitchings apologized to Watson and the Clemson coaches.
"As far as I know, everything has been settled," Doeren said. "I haven't seen it, don't know much about it, but [Kitchings] did come up and tell me that he apologized to their staff and Deshaun. It was a heat-of-the-battle moment and unfortunate. I think he handled it the right way."
Watson told reporters afterward, "A guy kind of swung at me and pushed me off. I just walked away. I don't know why he did it."
Watson went 23-for-30 for 383 yards and five touchdowns as the third-ranked Tigers improved to 8-0 (5-0 ACC).