Officers were made aware of the incident, which occurred outside school hours, after the girl died in hospital later that evening.
Initial inquiries suggest the child "perhaps suffered some sort of medical event" while running, a police spokesperson said today.
"Police's inquiries are on behalf of the Coroner who will ultimately determine cause of death," the spokesperson said.
The girl was a Year 8 student at Auckland's Baradene College of the Sacred Heart, which sees to the education of more than 1300 girls from Year 7 to Year 13.
"We have lost a Baradene student, and at the moment we are wrapping care around the family and our students at Baradene and supporting them all," school principal Sandy Pasley told The New Zealand Herald.
"We are absolutely devastated for the family, and we've got very sad students and staff also."
Pasley said she didn't know the circumstances of the girl's death.
She told the Herald today she wanted to guard the family's privacy, but she described it as "appalling" that people were speculating on social media about the cause of her death.
