Maha Al-Shennag drove a Toyota Kluger into a classroom of 24 students at Banksia Road Public School about 9:45am, injuring more than 20 people.
Two boys who were critically injured in the incident later died in Westmead Children's Hospital.
Two eight-year-old girls were also taken to Westmead in a stable condition, and one nine-year-old girl was taken in a serious condition.
It is understood Ms Al-Shennag's son is a student at the school.
Police will examine the vehicle involved to determine whether there were any mechanical problems.
