Witnesses reported injuries, including one woman who was trapped under concrete and many people bleeding.
TV footage and photos from the scene show damage to the rail car and extensive structural damage to the Hoboken station.
Images on social media show a train that appears to have gone through the bumper stop at the end of a track.
“The next thing I know, we are ploughing through the platform,” said passenger Bhagyesh Shah. “It was for a couple seconds, but it felt like an eternity.”
He said the train was crowded, particularly the first two cars, because they make for an easy exit into the Hoboken station and onto the Path train.
Passengers in the second car broke the emergency windows to get out.
“I saw a woman pinned under concrete,” Mr Shah told NBC New York. “A lot of people were bleeding; one guy was crying.”
A New Jersey Transit spokeswoman said it was not clear how many people were injured.
The train came to a halt in a covered area between the station’s indoor waiting area and the platform. A metal structure covering the area collapsed.
“It simply did not stop,” WFAN anchor John Minko, who witnessed the crash, told 1010 WINS.
“It went right through the barriers and into the reception area.”
The train had left Spring Valley, New York, at 7:23am local time and crashed into Hoboken Terminal at 8:45am, said NJ Transit spokeswoman Nancy Snyder.
The Federal Railroad Administration dispatched investigators to the crash scene, said Matthew Lehner, a spokesman for the agency.
Rail service was suspended in and out of Hoboken, which is directly across the Hudson River from New York City.
The station is a hub for commuters switching from the NJ Transit system to the Path system to head into Manhattan.
Hoboken, which is NJ Transit’s fifth-busiest stations with 15,000 boardings per weekday, is the final stop for several train lines and a transfer point for many commuters on their way to New York City.
NJ Transit provides more than 200 million passenger trips annually on bus, rail and light rail lines.
More than 100,000 people use NJ Transit trains to commute from New Jersey into New York City daily.