A video on Sky TG24 shows the escalator accelerating suddenly Tuesday evening, and the people riding down on it collapsing one onto another.
Italian media have reported that more than 20 people were injured when the escalator leading down to the metro station collapsed.
Footage taken by witnesses show the escalator running at an unusually high speed.
Seven people were seriously hurt in the accident at the city-centre Repubblica station.
Emergency services are at the scene and the station has been closed, Italian news agency Ansa reported.
2018-19 Season Preview: Boston Celtics
Oklahoma City was bounced out of the postseason last summer in the first round in a six-game series with the Utah Jazz . When you play for the Celtics, that expectation (to win a title) is always kind of there from everyone.
Dozens injured at party in South Carolina in floor collapse
Police said they received a 911 call at 12:30 a.m. about the cave-in and ambulances were quickly dispatched to the area. Tester said emergency responders were there in just minutes, and he saw people holding their arms or with bloody legs.
Irish border issue could sink Brexit deal, says European Union negotiator Michel Barnier
May said her proposal was an attempt to solve the issue of the Irish border, which has stumped negotiators for more than a year. But even an extension would not get rid of the EU's insistence that such a backstop must be agreed to secure a deal.
About 1500 CSKA fans were attending the match.
The malfunction is believed to have been caused by a large group of fans jumping on the escalator with force.
The Russian embassy in Italy later said that up to 30 football fans were injured.
CSKA Moscow is due to play against AS Roma in the Champions League later on Tuesday and hundreds of its supporters were on the move to reach the Olympic stadium.
La Repubblica website said the escalator broke after singing and chanting fans started to jump up and down on it.