There were 24 children in the classroom at the time.
Two boys, aged eight, were critically injured. They were taken to Westmead Children's Hospital where they died.
Three other children were taken to hospital but most other students from the classroom have minor injuries and were assessed at the scene, paramedics said.
Photos from the scene show the car, driven by a woman, 52, almost completely inside a classroom. There were 24 children aged between seven and 11 in the year three classroom at the time.