A serial platypus killer is apparently on the loose on the Victorian-NSW border, with three of the shy native mammals found dead in just over a month.

Two of the three dead platypuses found in the Albury Botanic Gardens were decapitated, apparently with a sharp object, according to wildlife authorities.

It has been condemned as a "despicable act of cruelty".

The deaths are not believed to have been caused by animal predators, such as foxes.

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The NSW National Parks and Wildlife Service is investigating and urged anyone with information to report it to authorities.

"NPWS is aware that three platypus were found dead in Albury Botanic Gardens in the last five weeks," she said.

"These animals appear to have been deliberately killed in a despicable act of cruelty to one of Australia's most loved animals.

"NPWS is working with Albury City Council and Wires [Wildlife Information Rescue and Education Service] to look into these incidents."

The spokeswoman said animal cruelty was a serious offence and anyone found guilty of the killings of the protected native animal could face jail time.

"It is an offence under the National Parks and Wildlife Act to harm native animals and penalties include a fine of up to $11,000 and or six months imprisonment."

Platypus numbers in the region are thought to be quite low.

Until the early 20th century, the semiaquatic creature was hunted for its fur, leading to its extinction in South Australia.

It is now only found in fresh creeks and waterways across eastern Australia, from Tasmania up to Queensland.

It is a notoriously shy animal and not often spotted in the wild.

Wildlife Information Rescue and Education Service Murray River secretary Hazel Cook told the Border Mail the decapitated platypuses had their heads cleanly cut off, which ruled out animal predators.

"There definitely was no fox involved," she said.

"You could see were it was cut, where the spine was cut."

Anyone with information is asked to call the NPWS Tumut office on (02) 6947 7025.