Her great-great nephew, Martin McCrae, of Stirling, Scotland, said he was "disappointed" to learn the gravestone had been placed on Dean's previously unmarked grave in the cemetery.
He was "seeking advice on what to do next".
After years researching his family tree, Mr McCrae informed the Winton Community Board in November he would be commissioning a gravestone to mark his ancestor's grave.
He had now written to the Southland District Council, requesting the unauthorised gravestone be removed "so the authorised one can be put in place".
"As far as we are concerned, our aim is to put a memorial in place that can provide some closure and healing for the family. We have sought this all along," he said.
Council area offices manager Chris Dolan said he was "disgusted" by the laying of an unauthorised gravestone without community board or council approval.
"From a personal perspective, I believe the laying of an unauthorised stone is, in fact, desecrating a grave site, which I take most seriously," he said.
Council staff inspected the site yesterday morning and removed an unauthorised wooden sign pointing to the grave.
"Whoever has done this has gone to a lot of work. It looks very professional."
The right to erect a headstone was that of the family and its wishes should be respected, Mr Dolan said.
The headstone was likely to be removed and the family-commissioned one installed by Gore firm McBride Bros in the next 10 days, he said.
McBride Bros spokesman Graham Stephen, of Gore, said he had assurances from all monumental masons in Southland they did not lay the stone.
The work on the gravestone, a granite panel in a concrete base, was professional and would have cost about $1000, he said.
Publican and Winton Community Board chairman John McHugh, who has lived in Winton all his life, said he was surprised by the appearance of the gravestone.
"I think I would hear most things that go on in the town, but this is news to me."
The previously unmarked grave site had long attracted interest from visitors, but should not be treated disrespectfully, he said.
Dean was found guilty on June 21, 1895, of murdering one infant in her care and sentenced to death.
She was hanged in Invercargill jail on August 12, 1895, the only woman to have been hanged in New Zealand.
