The crash happened shortly before 9:00 a.m. at a crossing in the 200 block of West Chestnut Street in Clayton.
Police say the driver of a 1998 Toyota Camry tried to cross the tracks as the freight train was coming.
The car was hit and pushed more than 280 yards down the track.
The woman and the baby, both residents of Clayton, were taken to Cooper University Hospital in Camden.
The names of those involved and their conditions were not released.
Police say the baby was restrained in a child safety seat.
The circumstances of the crash remain under investigation.
Officials believe the flashing lights at the crossing were operational and working properly at the time of the incident.