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 are also in hospital.
The pistol used in the incidents has been found by the police.
Clashes took place in the Tor di Quinto area close to the stadium, with rival supporters from Serie A rivals Fiorentina and Napoli throwing firecrackers and other objects at each other.
However, the police said in a statement that the three shootings did not appear to be linked to the broader clashes.
Officials then decided to delay the kick-off amid reports that Napoli fans did not want the match to go ahead until they had had confirmation that one of their fellow supporters had not been killed in the violence.
When match organisers went towards the Napoli fans with player Marek Hamsik they were pelted with flares and smoke-bombs.
The match eventually kicked off at 20.45 BST.