The punishment was confirmed in a statement from the league's governing body on Tuesday, following the April 26 meeting between the two sides.
Inter have been fined €50,000 for the incident, while a section of the ground will be closed for their final home game of the season - against Lazio on May 10 - as well as the opening home fixture of the 2014-15 season.
Elsewhere, Roma have been fined €15,000 after a section of their support threw missiles in the direction of the Milan fans in the game between the two sides on April 25.
Roma won 2-0 in the Stadio Olimpico, but the actions of their fans have been punished by the league.
Milan have also been sanctioned after their supporters retaliated and threw a missile back, with the club handed a €4,000 penalty.
