Supporters of the two Serie A sides were involved in a heated confrontation ahead of a fixture at San Siro on Wednesday.
Local authorities allege that a group of Inter followers attacked a bus carrying Napoli fans to the ground.
In the chaos which ensued, one man was hit by a car and, despite the efforts of medical professionals, passed away as a result of his injuries.
One other supporter is said to have been stabbed and three more left with heavy bruising.
Police services in Milan have called for action to be taken against those responsible.
They are seeking a ban on away support for Inter through to the end of the season and the closure of the Curva Nord section of San Siro until March 31.
Milan police chief Marcello Cardona told reporters at a press conference held on Thursday: “The clashes broke out abruptly.
“These ultras hit the coaches carrying Napoli fans with bars and sticks.
“There was an effort to flee and in the opposite lane, some cars passed by and an ultra from Inter, who had a stadium ban, was hit by an SUV.
“We still do not know who was driving and where they came from.
“Four Neapolitans were wounded slightly, one with a cut and then three with bruises.
“At this moment we have arrested two Inter ultras and are looking for another.
“We have identified three from the images and we do not rule out further arrests as what happened is very serious.
“I want to prohibit away followings for Inter until the end of the season and seek the immediate closure of the Inter Curva until March 31.”
In the wake of trouble outside the stadium on Wednesday, further issues were caused inside it once the action got underway.
Certain sections of the Inter support subjected Napoli defender Kalidou Koulibaly to racist taunts , with Carlo Ancelotti stating afterwards that he will remove his players from the field if a similar situation arises in the future.
He said, having seen Koulibaly dismissed amid disturbing scenes: “Koulibaly was certainly irritable. Usually, he is very calm and professional, but he was subjected to monkey noises throughout the game.
"We asked three times for some action to be taken, but the match continued. We keep being told play can be halted, but when? After four or five announcements?
"Maybe we have to take matters into our own hands next time and stop play ourselves. They’ll probably make us lose the game if we walk off, but we are prepared to do it.”