The odour of burning refuse wafted across the historic centre as the blaze, which began overnight, crept steadily from the site in the north-east of the city.
City hall said it had called the national civil protection agency and the environmental protection agency to an emergency task force meeting and was monitoring air quality in the area.
"We are waiting to see what the firefighters will determine caused the fire. What is certain is that this was not an unexpected or unforeseen disaster," said Natale Di Cola, from Italy's biggest trade union CGIL.
Residents in the surrounding neighbourhoods were advised to stay inside and a nursery next to the site was shut.
The environment minister warned back in January that Italy could be sanctioned by the European Union unless authorities in Rome and the Lazio region tackle the burgeoning waste disposal crisis.
The company in charge of collecting Rome's waste, Ama, has long been accused of failing to keep mounds of rubbish from overspilling onto the streets.
Thousands of protesters rallied in Rome in October over the capital's decrepit infrastructure, blaming Virginia Raggi, the city's first female mayor, for the garbage woes as well as a pitiful transport system.
"We have been denouncing the security risks - and fire risks in particular - for years, saying only the garbage that can be treated should be taken there, rather than it being stocked up," Di Cola said.
"From tomorrow, we will be in even hotter water. The site is out of action and Rome will be even more in crisis," he added.