Emergency services were called to Auburn South Primary School in Hawthorn East on Tuesday afternoon, after reports of a collision.
Police said a vehicle was travelling along Burgess Street when it is believed to have left the road and crashed through a fence near a sports court at the school just after 2:30pm.
The car collided into a table, where five students were sitting, Australian Broadcasting Corporation reported.
Two 11-year-old girls, one 10-year-old girl and a 10-year-old boy were all taken to hospital with serious injuries.
An 11-year-old boy was taken to hospital with critical injuries, and later died.
A 40-year-old Hawthorn East woman has been arrested and will be interviewed by police, while a primary school-aged child who was a passenger in the vehicle was unharmed.
Victoria Police Inspector Craig McEvoy said the driver was attempting a U-turn before veering off the road, and it appeared the crash was an accident.
He said the vehicle that crashed through the school fence had a green P-plate on it, but police have been unable to determine the license status of the woman.
"The ongoing investigation will take days, weeks, months," Inspector McEvoy said.
MA/PR