The two injured eight-year-old boys were rushed to Westmead Children's Hospital in critical conditions but there was little doctors could do and they died soon after.
Three girls were also badly injured.
"We were just doing work and all of a sudden we heard this big bang," year 4 student Mariam Issmail told AAP.
"(Students) were screaming, saying they wanted their mum, I want help," she said.
Authorities described the scene as "carnage" as paramedics and police responded and parents rushed to the site.
The 52-year-old woman behind the wheel was later charged with two counts of dangerous driving occasioning death and one count of negligent driving occasioning death.
Her licence was suspended and she was granted conditional bail ahead of an appearance at Bankstown Local Court on November 29.
Parents and students left flowers at the school gates on Tuesday afternoon and a brief vigil was held in the evening, including a minute of silence to remember the victims.
Extra counsellors will be on duty when the school reopens on Wednesday with support from counsellors for any student who wishes to attend, staff said on the school's Facebook page.