Kick-off at the Stadio Olimpico was delayed by 45 minutes as Napoli fans protested following the shooting of three men prior to the match in Rome.
Flares and missiles were thrown before Napoli captain Marek Hamsik was forced to speak with the ultras section of the support to calm the situation.
Rafael Benitez's men went on to win the game 3-1, capturing the trophy for a second time in three seasons.
However, Napoli have now been punished for the behaviour of their fans, receiving a €60,000 fine in addition to the order to play two matches behind closed doors.
A statement on the Napoli website read: "Regarding the game on Saturday, May 3 at the Olimpico between Napoli and Fiorentina for the Coppa Italia final, the Sports Court decided to impose a penalty on SSC Napoli of the obligation to play two games behind closed doors plus a fine of 60,000 euros.
"SSC Napoli will consider every form of defence."
