The alleged attack occurred in Limbadi, a small town of around 3,700 people, located 15 kilometres southwest of Vibo Valentia.
Mr Vinci, 42, was a former medical salesperson and had run as a candidate in the most recent town council elections.
Mr Vinci’s 70-year-old father Vincenzo was seriously injured in the blast and is currently fighting for his life in hospital.
Local police suspect the cause of the blast was an explosive device left in the Ford Fiesta’s boot and possibly activated via radio.
The motive for the apparent attack is not yet clear, although it took place in an area renowned for mafia activity.
Several publications reported that both victims of Tuesday’s apparent attack had a history of disputes with a local mafia-linked family.
They had been arrested in 2014 following a fight with members of the Mancuso crime group, according to Corriere della Calabria.
Mr Vinci’s mother Rosaria said the family would not be intimidated by the attack.
“We’re not scared,” she said.
“We’ve been fighting for our rights against the Mancusos for years.”