The North Island brown kiwi was hatched at Pūkaha in May 2011, with a rare genetic trait resulting in white feathers instead of the standard brown.
Manukura was seen as a "huge blessing" by the local Rangitāne o Wairarapa tribe, who saw her as a unifying symbol, according to the wildlife center's statement.
She even inspired a book by Joy Cowley, one of New Zealand's most prolific children's fiction authors, as well as a line of soft toys and other memorabilia.
"Over the past 10 years she delighted multitudes of people and in her own quiet way shone a spotlight on the precarious plight of kiwi in the wild," said Department of Conservation Wairarapa operations manager Kathy Houkamau, who was the center manager at Pūkaha when Manukura hatched. "She will be sorely missed."
Manukura was taken to specialist veterinarians in early December after her carers noticed she was not eating and losing weight, the statement said.
Vets found an unfertilized egg that the kiwi was unable to lay. Though their operation to remove it was successful, she needed more surgeries, and her health continued to deteriorate in subsequent weeks.
"Manukura is very much a part of the Pūkaha family and we have always felt so blessed to have Manukura to help us to tell the Aotearoa's conservation story," said Emily Court, Pūkaha's general manager, adding it was "one of the saddest days" the wildlife center had experienced. Aotearoa is the Māori name for New Zealand.
While white kiwi exist in the wild, they are considered so rare that seeing one in its natural habitat is highly unlikely.
According to New Zealand's Department of Conservation, there are about 68,000 kiwi left -- and 2% of unmanaged kiwi are lost every year. Threats include predators such as stoats, dogs, cats and ferrets.
Manukura is survived by her younger brother Mapuna, who is part of Pūkaha's captive breeding program.