However, the sanctions were suspended for one year and will only be implemented in case of a new offence during that period.
The written decision said Roma fans repeatedly chanted "wash them with fire from Vesuvius" during their team's 2-0 win over Napoli on Friday.
It said that chanting by Milan fans made reference to Naples and cholera during the first half of their game at home to Udinese on Saturday, forcing a warning to be broadcast over the public address system.
Torino and Inter supporters both made similar chants during their 3-3 draw on Sunday.
At the start of the season, the Italian federation announced automatic stadium closures for discrimination by fans.
The measure was intended to target racial discrimination but there was a twist when AC Milan were handed a partial stadium closure because of anti-Neapolitan chants by their fans during the home game with Napoli in September.
Ultras of both teams, who have long exchanged regional insults during games, criticised the decision and at their next home games, Napoli fans unfurled a banner which read: "Naples cholera-sufferers. Now close our curva!"
Inter Milan's Ultras, the Curva Nord, last week started a campaign inciting all supporters to break rules simultaneously with the intention of having an entire weekend where all the matches were played behind closed doors.
In response, the FIGC ruled that a sanction could be suspended for less serious offences or where fewer fans were involved.
(Writing by Brian Homewood; Editing by Alison Wildey)
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