A one-year-old boy and the man in his 40s died in the incident this morning in St-Liboire, east of Montreal.
Quebec provincial police spokeswoman Joyce Kemp says the homicide squad has been called in to determine exactly what happened.
She says the possibility the accident was a "voluntary act" is not being excluded for now.
The impact was so violent the SUV was cut in two.
Kemp would not confirm that the barriers at the crossing were working properly at the time of the accident, although a Via spokesman says the barriers were down and that the lights were flashing.
Kemp said the two victims were from the area.
Via Rail advised of delays on its Montreal-Quebec City route after the accident.