The France international punched Chiellini in the neck during Juve's 3-2 triumph over AC Milan in Turin on Sunday and, although the referee failed to see the action, TV evidence was used to determine the punishment.
Mexes was sent off during the encounter for two bookable offences, which resulted in a further one-match ban.
The 31-year-old will miss the league games against Udinese, Parma, Lazio and Fiorentina.
A Lega Serie A statement read: "The sporting judge punishes Philippe Mexes with a three-match ban for violent conduct in relation to an action that saw the Rossonero defender punch Giorgio Chiellini in the neck during a corner kick.
"Mexes is also handed a one-match ban for being sent off for a double booking during the game."
Mexes' absence is a blow for Rossoneri coach Massimiliano Allegri, who is without injured defenders Ignazio Abate, Daniele Bonera, Matias Silvestre and Mattia De Sciglio.
Milan have confirmed, meanwhile, that they will appeal against the decision taken by the sporting judge to close the San Siro for their next home game against Udinese on October 19 because of insulting chants by their fans towards rival supporters.