It happened at noon Sunday after the South Korean tourist slipped through the barrier set up to keep people away despite the siren indicating a train's arrival going off.
After the collision the person, who was not seriously injured, got up and left the place.
The incident caused the passenger train, arriving in Hanoi from the northern province of Lao Cai, to halt for two minutes.
Last weekend city authorities shut down coffee shops along the street as a safety measure.
Train Street has railway tracks running along Dien Bien Phu and Phung Hung streets in the heart of the old quarter with residential buildings barely feet away on either side.
The highly unusual sight fascinates both domestic and foreign tourists, especially selfie lovers.
After Vietnam reopened in March the street again began to draw tourists.
Cafes set up tables and chairs along the tracks and tourists stood in the middle to take selfies.