"It is vital that Aucklanders continue to have confidence in the museum as a safe place to visit," said the spokeswoman.
In a letter to the Herald, Catherine Hellyer and Dr Sean Sullivan said when they visited the museum yesterday it was shut due to a group of people suggesting they "would not" rather than "could not" wear masks.
"One of the women insisted we would be interested in hearing her argument, very closely we might add, masks were only protective of the wearer and she chose not to wear one."
The couple said this is a fundamental error and not wearing a mask can spread the virus more easily, especially when someone is asymptomatic or presymptomatic.
"We understand masks aren't foolproof, but they can reduce the amount of aerosol transmission and there is a good case that we should minimise any risk to others, especially the vulnerable members of our community. Not wearing a mask disregards this social obligation entirely," they said.