According to Macerata police, the shootings on Saturday morning were carried out in different parts of the town, including near the train station, leading to the injuries of six people, mostly African migrants.
Photos from the scene show a man being put into a police vehicle, wearing an Italian flag draped over his shoulders.
Police detained a 28-year-old Italian they believe to be responsible. The PD said he had stood as a candidate for the rightist Northern League at local elections previous year but had not received any votes.
The shooting may have been a response to the killing of a teenager, 18-year-old Pamela Mastropietro, who was eventually found cut up and placed in two suitcases, an incident that occurred days before, according to police.
The suspected shooter, an Italian man, was swiftly arrested, the police said.
Italian Premier Paolo Gentiloni said Italy would be "particularly severe against whoever thinks of nourishing this spiral of violence".
"The closeness of these two events makes you imagine that there is a connection", Carancini told Sky TG24.
Police said one of the injured foreigners needed surgery, but gave no further details.
Authorities asked members of the public to remain vigilant and to stay indoors while an investigation was ongoing. The number of victims hasn't been confirmed.
ANSA said witnesses reported that Saturday's drive-by auto was seen in the area where the woman's body was found.
Several racist comments calling for revenge attacks were posted on the Facebook page of the victim's mother in the run up to Saturday's shootings, Ansa reports.
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