STORY: Video posted online showed thick, black smoke billowing from the seven-story building.
An eyewitness reported hearing several explosions before seeing a huge column of smoke.
The president of IV municipality, Massimiliano Umberti, said two people suffered critical injuries and firefighters had difficulty entering dozens of apartments.
The fire broke out in the city's eastern Colli Aniene area at 14:00pm (1200GMT), Italy's Ansa news Agency reported. It said the cause of the fire was being investigated.