The officer was killed on Friday when a homemade explosive device was thrown into his vehicle by rioters outside a stadium in Catania during a match between Catania and Palermo, two Sicilian teams, said police.
Romano Prodi, the Italian prime minister, condemned the violence.
Italian news agencies quoted him as saying: "I feel it is my duty to say that we unfortunately need a loud and clear signal to avoid the degeneration of the sport that we, unfortunately and dramatically, are witnessing."
Güncelleme Tarihi: 20 Eylül 2018, 18:16
Another police officer was reported to be in a critical condition, and police said dozens of people with lesser injuries had been taken to local hospitals.
Luca Pancalli, Italy's Football Federation commissioner, called an emergency meeting in Rome, announcing he was canceling all games.
He said: "The decision to block the championships was immediate ... We cannot continue like this. What we're witnessing has nothing to do with soccer, therefore Italian soccer is stopping."
The federation postponed further league matches and cancelled Wednesday's friendly between Italy and Romania, as well as an under-21 friendly scheduled for Tuesday against Belgium.
During the riot Police fired tear gas which drifted into the Angelo Massimino stadium and caused the match to be temporarily suspended.
Violence continued after the game and the authorities held back hundreds of fans inside the stadium in the hope of avoiding further violence.
The ANSA news agency reported that nine Catania fans had been detained, but said none were suspected of killing the officer.
Giorgio Napolitano, the Italian president, released a statement saying the authorities should take a firm stand "against degenerations that demean the values of the sport and offend the country's civic conscience."
Police defended security measures at the game.
"We're talking about incidents that happened outside the stadium and after the game had already started," Piero Gambuzza, a police commander, said on Sky TG24 News. "Police did not allow anyone with explosives to enter the stadium."