A spokeswoman for the hospital said their injuries were being assessed and couldn't give an update on their condition.
A KiwiRail spokeswoman said the train driver was shaken but unhurt. There were 46 passengers on the Northern Explorer and another driver was brought in to continue the journey.
The KiwiRail spokeswoman could not say if the car had stopped on the crossing or was moving through it.
The accident site is close to the entrance of Horopito Motors, a car graveyard featured in the 1981 film Smash Palace starring Bruno Lawrence.