The bans come after the arrest in September of 19 leading "ultras" linked to both clubs, many of whom are believed to have connections with the 'Ndrangheta mafia.
As a result of this punishment, Inzaghi will miss the match from the bench, and Calhanoglu will be unavailable when Inter Milan host Verona on Saturday.
Inter Milan was fined 70,000 euros ($79,000) over the case, while AC Milan received a 30,000 euros fine.