The ruling centre-left Democratic party said Traini had stood as a candidate for the Northern League at local elections past year and also accused him of firing shots at one of their offices in Macerata before he was arrested.
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 his auto on foot.
Residents had been told to stay inside during the shooting and public transport was halted.
ANSA reported that the black vehicle used in Saturday's shooting spree had been seen in the area where the woman's body was found and also near where the suspect lived.
After the attack, Italian Prime Minister Paolo Gentiloni called on political leaders on all sides to stop a "cycle of violence".
Italy votes in national elections on 4 March, with immigration one of the key issues.
He is pledging to deport 150,000 migrants in his first year in office if his party wins control of parliament and he is named premier.
With about 28% support in the opinion polls, the anti-establishment 5-Star Movement is the most popular single party.
"We must be united against hatred", Carancini said.