Red-eared sliders are a popular pet turtle but are also listed as one of the top 10 invasive species in the world.
Members of the public found the turtle, believed to have recently died, in the garden earlier this week.
Dunedin City Council botanic garden team leader Alan Matchett said it was not permitted under the Reserves Act for the public to release animals into the garden, but it was not the first time people had tried.
Once a live turkey was left in the garden, and on another occasion a dead wallaby was found on Opoho Rd. People had also been seen walking a ferret and pet lamb on leads in the garden.
"Odd things turn up every now and again."
Department of Conservation biodiversity assets programme manager David Agnew said Doc advocated a more responsible way of disposing of a pet "if the owners had outgrown it or it had outgrown them".
Such animals could spread diseases to native animals and he encouraged people to report such incidents.
Maf Biosecurity New Zealand senior adviser communications Jaap Knegtmans said there were concerns about the impact on wildlife generally from the release of pets into the wild, as well as animal welfare issues.
Red-eared sliders left to fend for themselves in the wild often become deficient in vitamin E and calcium, causing their shells to soften and resulting in a slow death, he said.
The problem of them being released into the wild was worldwide and, as they were carnivores, they posed threats to fish, lizards and invertebrates.
The risk was less in New Zealand because the low temperatures meant they were unlikely to successfully breed in the wild.
Maf was working with related industries and government agencies to define the risk associated with exotic pets and had border controls to ensure pets that could "wreak havoc" on native flora and fauna did not get in, Mr Knegtmans said.
People needed to ensure they were fully informed before they bought turtles as pets, as they grew to the width of a dinner plate, weighed about 2kg and lived for 50 years, he said.
If people needed to dispose of the turtles and could not find another home for them, they should contact the SPCA, a local pet shop or the regional council for advice.
