"That night, my personal vehicle, parked at home, was set on fire and burned to the ground. Thanks to the intervention of the firefighters, whom I thank, the fire did not spread to the building," Murgia tweeted.
A video showing the mayor's burnt car was shown on local TV channel.
The incident came three days after the same episodes occurred in the "technical services" of the city administration, where two cars were also burned down, he added in a follow-up tweet.
There have been no reports of injuries after the incident, which is still being investigated.