The train reportedly went through ticket barriers and into the reception area of the train station.
Footages show extensive damage to the train carriages and station, with part of the building roof caved in.
Witnesses described a scene of horror at the station.
A huge emergency services operation swung into action following the crash, with firefighters and transport staff helping people from wrecked carriages.
Hoboken is across the Hudson River from New York City. Many people use the busy station to travel into Manhattan.
New Jersey Gov. Chris Christie confirmed there had been one fatality. The woman has been identified as 34-year-old Hoboken resident Fabiola Bittar de Kroon.
Chris Christie said she was struck by debris while standing on a platform.
He said the train’s driver – later identified as 48-year-old Thomas Gallagher – was in serious condition and being treated at a local hospital but was co-operating with investigators.
“We have no indication that this is anything but a tragic accident,” Chris Christie added.
In 2008, the Congress passed a law requiring all trains to install Positive Train Control (PTC) systems by the end of 2015.
However, most rail companies were unable to meet the deadline as the system is expensive and complex to install. Some rail lines – including New Jersey Transit – threatened to shut down completely if it was enforced. In response, Congress extended the deadline to install PTC systems to 2018.
Rail lines can then apply for an additional two-year extension to finalize updates and test the system. Safety targets for New Jersey’s transit trains say PTC installation should be completed by 2018.
According NJTransit’s most recent PTC progress report, none of the 440 trains on the New Jersey Transit rail line are equipped with PTC, nor have any employees been trained on the equipment.
Chris Christie said officials had no estimate on when the NJ Transit section of the Hoboken Terminal would re-open.
The structural integrity of the part of the building used for PATH trains has been deemed safe and was expected to resume service later on Thursday.
The National Transportation Safety Board (NTSB) vice chairman, Bella Dinh-Zarr, said the agency would be looking into whether there were any similarities between September 29 crash and one at the same station in 2011 that injured 34 people.
An NTSB investigation found excessive speed to be the main cause of the 2011 accident.
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