Fucci was walking across Piazza Indipendenza on Wednesday evening with Deputy Mayor Elizabeth Serra when the attack happened, Il Fatto Quotidiano reported.
The assailants were named by La Stampa as 67-year-old Walter Filippo Fedele, a former mayor of the town, and 53-year-old Lina Pontrelli.
The pair lashed out at Fucci with kicks and punches in protest at his refusal to authorise a street market in Pomezia, according to media reports.
A police officer who intervened in the ruckus was injured and taken to hospital along with Fucci and Serra, while the accused were arrested for injury and resisting a public official.
Thirty-three year old Fucci was elected on June 10th with 63 percent of the vote and is the first mayor for the Five Star Movement (M5S) in the region of Lazio.
On Monday another M5S politician became mayor, in the Sicilian town of Ragusa.