Traini had run for town council on the anti-migrant Northern League's ticket in a local election previous year in Corridonia, the party confirmed, but its mayoral candidate lost the race.
A Nigerian migrant was arrested in connection with her death.
The shooting came a day after a Nigerian man was arrested in the town over the brutal murder of 18-year-old Italian girl Pamela Mastropietro.
Police authorities said the attack appears to be "racially motivated".
One of those injured in the shooting has already been discharged from hospital; the other five are reportedly still receiving treatment but are all in a stable condition, although one is in intensive care.
A video posted by the il Resto di Carlino newspaper later showed the suspect with an Italian flag draped over his shoulders being arrested by armed Carabinieri officers in the city center, near where he apparently fled from his vehicle on foot.
Luca Traini, 28, a former nightclub bouncer with a Nazi tattoo on his forehead, is said to have draped himself in an Italian flag after the shooting spree with a Glock handgun in Macerata, central Italy, given a fascist salute and shouted "Long live Italy" before surrendering to the police.
Her boyfriend told La Repubblica they were waiting at a bus station when he saw a man pointing something at them from a black auto. And I heard a shot: "Boom".
Jennifer told the newspaper she arrived in Italy seven months ago and joined her boyfriend in Macerata.
"I have always been comfortable here".
They opened fire at various places, and shot people near the train station as they were chased by police.
Interior Minister Marco Minniti said the attack was part of a culture "of right-wing extremism with clear reference to fascism and Nazism" and deplored that the sole link between the victims was "the colour of their skin". According to official statistics, foreigners account for 9.2 per cent of the city's 43,000 residents.
Mr Salvini, in pole position to garner most votes in the March 4 election in alliance with media mogul Silvio Berlusconi, stopped short of condeming Traini saying the case was the result of too much illegal immigration.
Italian Prime Minister Paolo Gentiloni has spoken out to say "hatred and violence will not succeed in dividing us" after the shootings.
Far-right groups have been gaining in the polls, and the Northern League looks as though it may have a chance to govern as a junior member of a coalition with other right-wing parties.
Matteo Salvini, Lega's leader, condemned Saturday's shootings.
Hundreds of of thousands of migrants have landed in Italy in the last few years after crossing the Mediterranean Sea in smugglers' boats.