A 40-year-old woman had just collected her child at Auburn South Primary School in Melbourne's east on Tuesday when the incident occurred.
As she attempted to perform a U-turn, the car crashed through the school's fence and into a group of children sitting at a table.
An 11-year-old boy suffered critical injuries in the crash and died on the way to hospital.
Two 11-year-old girls, a 10-year-old girl and a 10-year-old boy were seriously injured and taken to hospital.
Three of the children were taken to the Royal Children's Hospital and two to Monash Medical Centre.
Victorian Premier Jacinta Allan said she was in parliament when she heard about the tragedy and felt instantly shaken.
"My stomach just lurched and I think any parent, we've all done the school pick-up, the school drop-off. Any parent of a of a child at a primary school yesterday felt particularly sick," she told Nine's Today show.
"I've got a little boy in grade five and it really does bring it home about how how difficult this will be today for the school community."
The driver of the vehicle, from Hawthorn East, was arrested and interviewed by detectives.
However no charges were laid and she was released overnight pending further inquiries.
The woman and child in the car were not injured.
The street was closed as police set up a crime scene at Auburn South Primary School. (Joel Carrett/AAP PHOTOS)
Detectives worked into the evening to investigate the circumstances of the crash, which Inspector Craig McEvoy said appeared to be a "tragic accident".Â
"It's really tough for everybody involved, from the community, the school community, the locals, the first responders, ambulances and police," he said.
"These events are always hard where there's there's death and serious injury, but especially difficult when there's children involved."
The car had a green P-plate, but Insp McEvoy said he was not certain of the woman's licence status.
Premier Jacinta Allan gave her condolences, saying the incident cast a "dark shadow", while opposition leader and local MP John Pesutto said it was a "painful shock".