It is feared at least 100 people have been injured, many critically.
People are believed to be trapped in the debris.
Local media are reporting at least three deaths.
Eyewitnesses say the train, coming in from New York State, overshot the end of the platform.
It crashed through ticket barriers into the concourse of the station.
According to reports, the carriages concertina-ed upwards and shattered the station’s glass roof.
Emergency crews are at the scene, including at least 20 ambulances.
Images uploaded to social media show severe damage to the train and widespread structural damage to the station concourse.
Injured people can be seen being led away for treatment.
Commuter hub for New York City
The New Jersey Transit Authority says services have been suspended in and out of the station while the emergency is ongoing.
Hoboken is six hours behind Central European Time. The crash happened iat 8.30 am, right in the middle of the Thursday rush-hour.
Many commuters use the station to travel into Manhattan for work. (Euronews)