In Rome a group of about 200 people, some wielding rocks and clubs, attacked a police barracks, setting cars on fire and smashing the building's windows.
Three top league matches had earlier been called off after a policeman killed a 26-year-old man during a spat between supporters of Rome club Lazio and Turin's Juventus at a motorway rest stop near the Tuscan city of Arezzo.
Outside Rome's Olympic Stadium, hundreds of fans threw firecrackers, set up street barricades and clashed with police.
About 10 officers were injured, ANSA news agency reported.
In Milan, Lazio fans threw rocks at a police station in protest at the shooting and marched towards the city centre shouting “Assassins!” at security forces, although the protest subsided in the evening.
Shooting an ‘accident’
Police said the shooting was accidental.
“It was a tragic error,” the police chief in Arezzo, Vincenzo Giacobbe, said in a statement.
“Our agent intervened to prevent the scuffles between two small groups of people…from degenerating,” he said.
“I express my deep grief and sincere condolences to the family of the victim.”
He later told reporters the policeman had fired two shots, one of which fatally wounded in the neck Gabriele Sandri, a disc jockey from Rome who was in a car of Lazio fans.
“They killed my brother,” Cristiano Sandri shouted at reporters at the police station in Arezzo.
As news of the death spread among supporters gathering at stadiums across Italy, the national football league postponed Lazio's match with champions Inter Milan, due to kick off at 1400 GMT (0100 AEDT Monday).
In the northern city of Bergamo, Atalanta's match with AC Milan was abandoned after supporters tried to smash down a glass barrier keeping them from the pitch.
Fearing more trouble, authorities later also called off an evening match between Lazio's city rivals AS Roma and Cagliari but hundreds of angry fans gathered outside Rome's Olympic Stadium.
Crowd trouble also marred a third division match in the southern city of Taranto.
Italian Prime Minister Romano Prodi called the violence “very worrying” and said he had asked for a full probe on the circumstances of the Arezzo shooting.
Italy is battling a serious soccer hooligan problem and suspended all soccer 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, which was a contributory factor in Italy being beaten by Ukraine and Poland in the race to stage the Euro 2012 soccer championship.
Officials said last month that fan injuries caused by violence around Italian stadiums had been cut by 80 per cent from last season but that it was difficult to combat violence away from the grounds.