Senior Sergeant Dan Cleaver said the accident occurred at 4pm at a carpark on the periphery of Kamo Intermediate School.
"There has been a crash involving a toddler and unfortunately they are now deceased," Mr Cleaver said.
The toddler's mother was present at the time, he said.
The carpark is off Lincoln Place, away from the school's main entrance, and is used by the public after hours, as well as staff.
Police were still investigating the circumstances around the crash but described it as "low-speed".
A handful of witnesses were still being interviewed, Mr Cleaver said.
The serious crash unit was at the school.
NZH