The Wakatipu herd produces most of the largest whitetail trophies in the South Pacific and up to 30 record-book bucks a year.
However, hunters posting photos with trophies online had resulted in more overseas hunters, particularly Australians, wanting to bag their own in Queenstown, the report said.
"Demand for trophies from the Wakatipu herd has increased exponentially in the past five years, owing to increased exposure on social media, and this shows no sign of abating."
The herd's production capacity could not keep pace with demand, so hunters were taking young bucks, some in velvet, meaning a "significant number" were dead before they could be considered a trophy, or breed.
Increasingly, 2-year-olds were being taken and "displayed on social media".
There were also "significant difficulties" with monitoring "brazen" illegal hunting of the herd on public and private land, also being boasted about on social media.
Conservation board chairman Pat Garden said the Mt Aspiring National Park management plan was due for review, and the whitetail herd would be discussed.
While its presence contradicted the National Parks Act, there was a "very committed group of the public" keen to see it retained.
Conversely, Forest & Bird was "strongly of the view" expectations in the Act should be upheld and the herd exterminated as far as possible, he said.
Forest & Bird Otago Southland regional manager Sue Maturin said whitetail were known to affect conservation values which might impact the health of invertebrate and wildlife populations, like mohua.