The 49-year-old woman, who is homeless and originally from Romania, was attacked in the town centre on via Mecenate, just metres away from the city's crowded September fair, Corriere della Sera reported on Thursday.
A man, thought to be the woman’s partner, reportedly doused her in alcohol before setting her alight. Police are now searching for the 60-year-old man, who is also homeless and from Romania.
According to reports, the couple had been arguing before the attack.
After the attack, the badly burned woman reportedly went into a bar to ask for help, saying that her partner had attacked her. The bartender then alerted emergency services.
The woman has been transferred to a burns unit in Genoa where she is said to be in a serious condition.
Reports of women being attacked by their partners in Italy continue to hit headlines.
In March, an Italian lawyer was sentenced to 20 years in prison for hiring two men to throw acid on his former girlfriend's face, severely disfiguring her.
On Tuesday this week, La Repubblica reported that a man in Alatri, south-east of Rome, attempted suicide after stabbing his wife to death following an argument.
And on Monday, a man suffering from senile dementia in Palermo, Sicily, killed his wife using a coat hanger.