The incident occurred during the sides' 1-1 draw in Turin on Tuesday, a result which left leaders and champions Juventus just one point ahead of title rivals Roma.
Serie A disciplinary officials regularly resort to video replays to sanction infringements not spotted the match referee.
A statement by Serie A officials said "television images showed the Nerazzurri player...lashing out with his elbow to the head of his opponent, who slumped to the ground in pain."
It described the gesture as "violent conduct" for which "Juan Jesus has been disciplined with a three-game suspension."
A further one-game ban was added because he had also picked up his fourth booking of the season during the game.