Napoli's Senegalese defender Kalidou Koulibaly says racist fans must be "kept out of stadiums forever".
Koulibaly and team-mate Victor Osimhen detailed on social media the racist abuse they received from Fiorentina fans during Sunday's 2-1 away win.
Nigeria forward Osimhen called for supporters to "understand how disgusting it is to hate an individual because of the colour of their skin".
Fiorentina also released a statement to condemn the incident.
Italian newspaper Gazzetta dello Sport reported that Andre-Frank Zambo Anguissa, on loan in Naples from Fulham, was also targeted by home fans.
"Fiorentina expresses the most firm and harsh condemnation for the episodes of racism that took place yesterday during the match against Napoli," the Serie A club said in a statement.
"General Manager [Joe] Barone, already after the match, personally apologised."
Fiorentina say CCTV footage from the game will be provided to the authorities to help identify the "culprits".
The Italian Football Federation [FIGC] has opened an investigation into the incident.
It follows an investigation being opened into alleged racist chants by Lazio fans aimed at AC Milan's on-loan Chelsea midfielder Tiemoue Bakayoko.
Napoli came from behind to maintain their winning start to the Serie A season, thanks to goals from Hirving Lozano and Amir Rrahmani.
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