Milan's match against fourth-tier side Pro Patria was abandoned when Boateng, in possession on the left wing in the 26th minute, suddenly picked the ball up and kicked it towards the stand behind him.
The Ghana midfielder then tore off his shirt and walked off the pitch, followed by the rest of the Milan side.
Italian Football Association president Giancarlo Abete branded the incident "unspeakable and intolerable" and an offence to Italian football and announced an immediate inquiry.
Piara Powar, executive director of European anti-discrimination group FARE, demanded strong action from the Italian FA.
He told the Press Association: "We salute Kevin-Prince Boateng for his actions and his team-mates for their support. This is the not the first time a player has walked off in Italy - if the situation continues it may not be the last.
"Italy, as much as any country in Europe, has a serious problem of racism to deal with. Football infrastructure is in need of renewal and at serious odds with the changing nature of Italian society. We look forward to strong action by the FIGC (Italian FA)."
Russia have also had their problems with racism. A Zenit St Petersburg fans group issued a statement before Christmas calling on the Russian club not to sign black or gay players.
"2013 starts in Italy as 2012 finished in Russia with a stark example of what has become the biggest social challenge facing football," Powar added.
Milan's website said there was also racist abuse by "a minority of Pro Patria fans" at Mbaye Niang, Urby Emanuelson and Sulley Muntari.
Boateng said on Twitter after the game: "Shame that these things still happen... #StopRacismforever."
Abete said in a statement on the Italian FA website: "No sanction or measure can erase the disdain for an unspeakable and intolerable episode.
"We must react with force and without silence to isolate the few criminals that transformed a friendly match into an uproar that offends all of Italian football."
Milan coach Massimiliano Allegri told reporters: "We are disappointed and saddened by what has happened.
"Milan play for the right to respect all players. We need to stop these uncivilised gestures.
"We are sorry for all the other fans who came here for a beautiful day of sport. We promise to return, and we are sorry for the club and players of Pro Patria, but we could not make any other decision.
"I hope it can be an important signal."
The match was goalless at the time, with Muntari having had a goal disallowed for offside.