The train reportedly went through ticket barriers and into the reception area of Hoboken station.
Images show extensive damage to the train carriages and station, with part of the building roof caved in.
People are said to be trapped in the wrecked carriages.
A spokeswoman for New Jersey Transit, Jennifer Nelson, told reporters that 20 ambulances had arrived at the scene to take the injured to hospital.
Ben Fairclough, a witness who was at the station, told the BBC: “I wasn’t on the train, but I arrived just after it happened. There was water coming down off the roof and people climbing out through the windows.
“There were people sitting down with blood coming from their head. There were lots of injuries.”
Commuter Mark Cardona described a “horror scene” at the station.
“I was on my way to work. I was halfway along the platform when I saw a runaway train coming at me.
“It went full speed into and then through the building,
New Jersey Transit posted on Twitter that the service out of Hoboken station had been suspended as a result of the crash.