Footage posted on social media showed the escalator suddenly picking up speed and throwing people to the ground as they reached the bottom.
Reuters Yara Nardi
Footage on social media shows people being crushed at the bottom of the escalator as it runs out of control.
AGI reported that around 15 CSKA fans had been hurt, two of them seriously. Emergency officials are responding to the scene.
There were also reports of one Russian visitor being stabbed with a knife, but they were later refuted by the Italian embassy in Moscow.
The malfunction is believed to have been caused by a large group of fans jumping on the escalator with force.
Many fans sustained cuts to their legs by shattered metal and glass.
The prefect's office put the number of injured at 20, mostly Russians in town for a Champion's League soccer game between CSKA Moscow and Roma.
An escalator at Rome's Repubblica station collapsed this evening injuring tens of Russian football fans on their way to the Olimpico Stadium.