The Nerazzurri have also been fined for alleged territorial discrimination against southern supporters, while Roma fans have been punished for throwing missiles at Milan fans.
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 has been fined 50,000 euro 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 has been fined 15,000 euro after a section of its 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.
Milan also has been sanctioned after its supporters retaliated and threw a missile back, with the club handed a 4,000 euro penalty.