A senior police source in Rome said the victim, 26-year-old Gabriele Sandri, was killed inside a car of Lazio fans when a policeman from a patrol stationed nearby opened fire to stop the clashes.
"The policeman said he shot in the air," the source told Reuters.
"It will be up to the investigators to establish that."
The car was taken away for inspection by police and the parking lot outside the motorway restaurant was cordoned off, witnesses said.
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"The policeman said he shot in the air. It will be up to investigators to establish that."
Police sources in Rome |
Sky TG24 TV quoted witnesses as saying the Juventus fans were traveling in two vans from Naples on their way to Parma for the Parma-Juventus match.
Romano Prodi, Italian Prime Minister, said he had been informed of the incident and told reporters: "Certainly these events are very worrying."
The Serie A match between champions Inter Milan and Lazio was postponed after football officials held urgent talks with the government.
The rest of the league games scheduled for Sunday, including a Juventus match at Parma, were rescheduled to start 10 minutes late with players and referees wearing black armbands.
Atalanta-AC Milan match also cancelled
Scuffles between fans and police erupted at the stadium in the northern city of Bergamo where Atalanta were hosting AC Milan, as news of the death of the Lazio fan spread.
Two policemen were slightly injured, before the match itself had to be stopped after just seven minutes as fans tried to break through barriers around the field.
Atalanta players went over to the fans behind the goal in a bid to calm them down and shortly afterwards the referee led all the players off the pitch.
Two holes were created in the barrier next to the goal by fans who covered their faces with scarves.
Order was then quickly restored, but the match was called off and will be rescheduled for a later date.
Italian football is battling a serious hooligan problem and suspended all matches for a period in February when a policeman was killed in riots outside a top-flight match in Catania.
Sporadic violence has continued in recent months despite the security crackdown prompted by February's incident.
Last month officials announced that fan injuries caused by violence around stadiums had been cut by 80 per cent from last season but that it was difficult to combat violence away from the grounds.