Photos showed a number 63 bus engulfed in flames on the Via del Tritone, a busy shopping street that leads past the Rinascente department store.
Witnesses told La Repubblica that they heard a loud explosion, then saw a column of smoke rising into the air.
Passengers managed to flee and no one on board was injured, according to a statement from Rome's public transport authority, Atac, which said that the 15-year-old bus was completely destroyed.
However, a passerby was treated for burns to her arm, RomaToday reported.
As thick black smoke billowed from the bus, more bangs were heard as the tyres burst. Firefighters cordoned off the street and instructed people in nearby buildings to keep their windows closed.
The incident was a particularly dramatic example of a phenomenon with which Romans are already familiar. Fires broke out on eight other buses in the first four months of 2018, with a regular frequency of two a month. May is on track for the same pattern after a second bus caught fire later on Tuesday in the south-eastern outskirts of Rome, bringing the 2018 total to ten.
2017's record is even worse, with as many as four bus fires in a single month. A total of 22 incidents were reported last year.
To date no one has been reported injured in any of the fires, which are common enough to have their own nickname among Romans: "flambus", a reference to Trambus, as Atac was formerly known.
As one journalist commented: "Only in Rome does a bus explode in the heart of the city and people immediately blame Atac, with no thought of terrorism. It says a lot about our emergencies."
Repeated internal inquiries failed to stop the problem, which drivers' unions put down to an ageing fleet of buses and lack of maintenance.
The regional secretary of the Faisa-Confail union, which has called strikes over the issue in the past, told RomaToday that "it's not safe with Atac".
"By this point drivers can only pray that nothing happens, and we don't even want to think about what will happen when it starts getting warmer," Claudio De Francesco said after the fifth fire of the year in March.
After Tuesday's incident, Atac said that it had immediately opened another investigation and stressed that it had recently stepped up fire-prevention measures on its fleet, "which unfortunately has a very high average age".
Bus fires are down by around 25 percent in the first four months of 2018 compared to last year, the company added.
Photo: Chris Junker/Flickr