The whale was found last Thursday afternoon and was then inspected and buried the next day.
Penguin Rescue sanctuary manager Rosalie Goldsworthy said the whale was beautiful and it was sad it had died.
It was located about midway between the Moeraki village and the Moeraki Boulders.
Department of Conservation Coastal Otago biodiversity ranger Jim Fyfe said Doc was called about a beached whale at Moeraki Beach at about 4pm.
The whale was reported dead at the time.
"We contacted Moeraki rūnaka and researchers and Doc specialists were sent photos to identify the species.
"As it would be getting dark soon, we waited until Friday to go out to the site."
The whale was identified as a dwarf minke whale calf which was 2.2m long.
Last Friday, Doc staff met iwi on site and took measurements and photos.
The decision was made to bury the whale and appropriate tikanga (customs) were observed.
It was thought the young female calf died of natural causes. It was emaciated, so it might have been a case of being separated from its mother.
If anyone came across a beached whale, or any injured or dead native wildlife, they should call the Doc hotline 0800 DOC HOT (0800362-468), Mr Fyfe said.
Doc would ask for a description of the situation, including the number and type of animals as well as a specific location.
Photographs were also helpful, so it could identify the species.
