Dramatic Twitter footage posted by a Russian fan shows the escalator running at incredible speed, causing people to pile up and crash into each other at the bottom.
The station has been closed and emergency services are on scene, where injured fans are being stretchered to safety.
Separately, one CSKA fan was slashed with a knife during clashes between opposing fans outside the Stadio Olimpico, the ANSA news agency reported.
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On Sunday, Foreign Minister Adel al-Jubeir described his death on Fox News as a "murder" and a " tremendous mistake ". The deal "will allow us to intervene to rebalance the market in any appropriate time from January onward", he said.
Only one of the people hurt is in a serious condition, a spokeswoman for Rome's civil protection department said, while the others were being treated for less serious injuries.
Witnesses say the football fans had been singing and jumping before the escalator gave way and footage shared on social media shows people piling up at the bottom.