Italy's special police unit Digos is leading an investigation looking into the possibility that anarchists set fire to the cars on the eastern outskirts of the Italian capital in the early hours of Monday, a security source said.
Tesla cars have become targets for vandalism across several countries in response to Musk's right-wing activism.
The tech tycoon, who also owns social media platform X, joined US President Donald Trump's administration and has come out in support of far-right parties in Europe.
Commenting in a post on X that made reference to the Rome fire, Musk used the single word "terrorism".
Drone images of the fire showed the burnt-out remains of cars lined up in a parking lot, with two rows of vehicles back-to-back and a third row some distance away.
The fire brigade said in a statement that the blaze broke out at around 4.30am local time. The dealership was partially damaged, but nobody was injured.
Italy's Deputy Prime Minister Matteo Salvini, leader of the right-wing League party, also took to X to express his support for Musk. "Too much unjustified hatred against the Tesla car company," he posted.
"The season of hate and conflict must come to an end as soon as possible. My solidarity goes out to Elon Musk and to all the workers who have been threatened and attacked," Salvini said.
Two Tesla stores and some cars were also vandalised in Sweden's capital Stockholm and coastal city Malmo on Monday, several Swedish media outlets reported.
Orange paint was sprayed on a Tesla store in Malmo, public broadcaster SVT reported, adding police had detained four people and were investigating the motive behind their actions.
"A patrol was alerted to a store on Boplatsgatan due to someone painting a building and cars with orange paint," the Malmo police said in an online statement, referring to a street near the city centre.
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