The incident took place on Via dei Fori Imperiali, the road that runs from Piazza Venezia to the Colosseum, on Monday evening, a time when the area is packed with sightseers.
Armed with a kitchen knife and shouting, the 32 year-old Brazilian man reportedly spread panic among the crowds of sightseers, sending them running scared.
He then allegedly grabbed a 27-year-old Italian girl and forced her to kneel down. While pointing the knife at her throat, he is said to have yelled: "I've been sent by God."
One witness told La Repubblica, “It was like something from Isis. He made the girl kneel down, just like you see in the terrorist films, and then he held the knife to her throat. All that was missing was the orange jumpsuit.”
Police were on the scene immediately and intervened to free the girl, who escaped shaken, but unharmed.
The police then tried to stop the man but he leapt over a barrier into a crowd of tourists.
A chase on foot ensued before two police officers finally caught up with the man near Piazza Venezia and managed to disarm him.
He was arrested and his identity is currently being ascertained by the police. The young girl was taken to Santo Spirito hospital in Rome, suffering from shock.
The incident comes at a time when the terror alert in Italy is high, and just days after Isis claimed responsibility for a car bombing at the Italian Embassy in Cairo, which left one dead.
Speaking after the incident, Ignazio Marino, the mayor of Rome, thanked police for their efforts in stopping the man.
"They showed courage and readiness," he said. "These actions generate pride and trust in our law enforcement units among Roman citizens and me personally."