The incident occurred at the Repubblica station at about 7 pm (local time), during "a time of maximum overcrowding", Il Messaggero newspaper reports.
An extremely graphic video of this incident, which features strong language, was published on Telegram.
"A group of CSKA fans went upstairs from the station. At that moment, the escalator collapsed. At least eight of them were injured. The number of victims may increase," a spokesman for the Roman police told Sputnik, adding that all those injured have been hospitalized.
"We heard a roar as it came down," one of the eyewitnesses said. "There was no time to save."
One witness also claimed that one of the victims had to have his leg amputated.
According to La Repubblica, at least 20 were wounded, with one person ending up "with the semiamputate foot."