A video of the event went viral and appears to show people being spit out onto the floor by the fast-moving escalator.
The footage appears to show a packed escalator moving at an alarmingly fast speed, flinging riders off and causing them to pile at the bottom of the steps with no place to move.
"It was a unusual accident", Rome firefighters' commander Giampiero Boscaino was quoted as saying by ANSA, adding that it was too early to speculate about what caused it.
Many football fans are among the victims as the incident occurred at the Repubblica metro station in the Italian capital shortly before CSKA Moscow's match against AS Roma in the UEFA Champions League.
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Rome Mayor Virginia Raggi visited the metro station and said the local transport authority had opened an investigation. One Russian fan was stabbed with a knife, and two others were hurt in clashes with other supporters.
Incidents on escalators have caused injuries, and even deaths, around the world. One of the fans is listed in serious condition.
Contrary to initial reports, the Russian fans were not jumping and celebrating on the escalator when the collapse happened.
"A group of CSKA fans were going down into the station".
Rescuers give assistance to a person who was wounded after the escalator started running too fast before crashing.