One of the men was taken to the Villa San Pietro hospital in a critical condition after being hit in the chest while the two others were shot in the arms and also in hospital.
The pistol used in the incidents has been found by the police, the AGI and ANSA news agency said.
Clashes took place in the Tor di Quinto area close to the stadium, with rival supporters throwing firecrackers and other objects at each other ahead of the game which was due to kick off at 1900 GMT but was delayed by 45 minutes.
However, the police said in a statement that the three shootings did not appear to be linked to the broader clashes.
Maurizio Beretta, the Serie A president, said he had made a "heartfelt appeal for responsible behaviour" from the supporters.
Piero Grasso, the president of Italy's Senate, who is due to present the trophy at the end of the match, declared those responsible were "delinquents, not supporters."
"A game of football cannot be turned into a war between rival gangs," he said.
The website of daily newspaper La Repubblica reported a total of six people had been injured in the clashes. ANSA put the tally at 10 and said four were in hospital.
Napoli fans protested after arriving at the ground, without singing or displaying any banners or flags.
Discussions took place pitchside about whether to play the game, and when match organisers went towards the Napoli fans with player Marek Hamsik they were pelted with flares and smokebombs.
(Reporting by Gavin Jones, editing by Alan Baldwin)
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