New Jersey Gov. Chris Christie told reporters the fatality involved a woman who was struck by debris from the crash while she was standing on the platform.
She was later identified as 34-year-old Fabiola Bittar de Kroon. She had moved to the area from Brazil earlier this year, the Associated Press reported.
Christie told CNN that 114 people were injured and that the train's engineer, who was also "critically injured," had been released from the hospital and was cooperating with law enforcement officials in the investigation.
The crash occurred when Train No. 1614 came into the station at high rate of speed, burst through the barriers, and breaking into the interior wall of Hoboken terminal, Christie said.
The train, coming from Spring Valley in New York, was on the Pascack Valley Line.
At least three people were in critical condition and eight people were in serious condition, an official from Jersey City Medical Center told reporters. There were also 40 walk-ins at the center.
"We don't have any reason to believe there will be any more fatalities," Christie added.
Two days after the incident the train still remains in the terminal, blocking the tracks for other trains, due to "environmental and structural issues."