The cloak, made in the traditional method by renowned weaver Garry Grace, is tan with black tassels and hand-woven fabric with embroidered detailing on the bottom.
"It represents about three months of work."
Dods said it was "distressing" that someone had stolen from the gallery, and the thief would have been "ridiculously lucky" to get away undetected.
The gallery has security cameras, but at the time of the theft the camera covering that area was not working, which the thief had no way of knowing, Dods said.
"They just brazenly don't care."
Curator Hannah Amu said the gallery implements strict tikanga about how they respect the taonga that comes in.
"When I first heard it was stolen it was extremely devastating.
"We've had reports that it was a Māori man, which upsets me because I am Māori. It has extra connections to ideals and ways that you're supposed to carry yourself.
"On a taonga level, korowai is extremely important."
Although the gallery does sell items, its first priority is supporting Māori and other New Zealand artists, and keeping the "sacredness" of the items.
"I consider that korowai to be tapu. He's preying on such important protocols and tikanga."
Amu believed it would "very unlikely" the thief would be able to sell the cloak.
A number of reports say a 1.70m Māori man with a tattoo on his right cheekbone was trying to sell a korowai outside Burger King on the corner of Tory St and Courtney Pl in the central city on Tuesday night.
