It's not the first time the huia have been targeted by thieves. In 2012 two tail feathers were stolen from the male.
"It's pretty clear the thieves knew exactly what they were after this time since they didn't touch the male as they must have known its tail feathers weren't genuine," Wadsworth said.
Gallery volunteer Murray Holden said he had been told that a pair of huia had recently sold in London for $30,000.
"This very sad, not only for the gallery but for the people of Dannevirke, it's part of the district's heritage," Holden said.
There are concerns regarding damage to the stolen female. "When we had the feathers replaced on the male, we asked the repairer if he could fix the feathers on the female as they were very ruffled, but he said she was too fragile to touch."
The pair of birds were donated by the Galloway family more than 30 years ago and had been the gallery's biggest drawcard. The birds were shot in Pohangina Valley in 1889 and mounted as a wedding gift for a local couple. They were reported to be the last huia in the valley.
The huia are highly prized for their unique white-tipped black tail feathers. In 2010 a tail feather sold for $8400 at Webb's Auction House in Auckland, which was believed to be a record for a bird feather at that time.
The huia is one of New Zealand's best-known extinct birds because of its bill shape. The female has a long, curved bill while the male has a shorter, straighter bill. Huia were regarded by Māori as tapu and the wearing of its skin or feathers was reserved for people of high status.
The Gallery of History is offering a reward for the safe return of its huia. So far there has been no response.