Eyewitness News is told the woman and the girl, believed to be her daughter, were hurt.
Officials say the woman driver, in her 40s, sustained a broken leg. The 12-year-old girl had a broken ankle.
They were both taken to Jersey City Medical Center with non life-threatening injuries.
Service was suspended between Newark and the World Trade Center for an hour while the car was moved off the train tracks.
The cause of the crash is under investigation, although it appeared the driver lost control of her car, went through a fence and flipped onto the tracks.