The animal was about ten feet tall and was pinned to two of its legs. It is unclear if the badger was already dead when the nails were driven.
A member of the public found the dead animal on the morning of August 18 and alerted police.
Investigations are being carried out by the North Wales Police Rural Crime Team.
An autopsy will be performed on the badger to determine the cause of death.
PC Richard Smith commented: “We cannot yet confirm what was the cause of death for this animal, but we have sent the body for an autopsy.
“Unbelievably badger chasing is still practiced in North Wales and we will continue to work with partners to tackle heinous incidents like these.”
Anyone with information about the case is urged to contact the police by calling 101, quoting the reference number Z121155.
Alternatively, you can call Crimestoppers anonymously on 0800 555 111.
According to the Badger Trust, thousands of British badgers are illegally attacked each year.
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However, animals continue to be a target in some parts of Britain.
The Badger Trust said: “Despite their unrivaled protection, thousands of badgers each year across the UK face dire fates due to both barbaric acts of cruelty and the illegal use of machinery in otherwise legal activities such as development and agriculture.
“The most common wildlife crimes involving badgers include: settlement interference, development-related, agriculture-related, land clearing, shooting, badger baiting, poisoning, trapping and gassing.”
The Badger Trust has advised 30 police forces in England and Wales on wildlife crime since 2017.
He is pushing for tougher sentences and recently held a meeting with the Prime Minister’s special adviser for the environment.
He commented: “The current sentence is not a real impediment, a potential sentence of up to 6 months does not work, and good behavior offenders only serve a few months.
“It is necessary to increase the penalties for crimes that involve cruelty and suffering.”
Attacking badgers is one of the current priorities of the UK Association for Action Against Wildlife Crime (PAW UK).
The government-backed group works with a number of charities and interest groups.
The delegated administrations of Wales, Scotland and Northern Ireland contribute to PAW UK.