Senior Sergeant Steve Aitken, of Dunedin, said the girl had gone out on the boat with her 48-year-old father and a male friend, also aged 13, in the early afternoon.
He said it was thought the boat's engine started to fail and cut out about 300 metres from the shore.
"The boat became swamped before capsizing."
The man and boy made it ashore together, while the girl was found on shore about 30 minutes later.
"Tragically, resuscitation attempts to revive her were unsuccessful," Mr Aitken said.
Acting Sergeant Steve Griffiths, of Balclutha, confirmed CPR was carried out, but the girl was unable to be revived at the scene.
Emergency services from Balclutha and Owaka responded to the incident.
Acting Sgt Griffiths said all three were wearing life-jackets.
Police did not expect to release the girl's name until tomorrow at the earliest.
