The Brisbane couple are planning to marry in Waipu next January. Photo / 123RF
"I do not wish to offend either of you and I thank you for letting me know that it is a same-sex wedding," it said.
"Even though as individuals you are both fabulous and amazing people, I must follow the integrity of my heart and beliefs.
"Our Government has legalised same sex marriages, but it is not my belief that it is correct, therefore I will not support it and cannot make your wedding cake for you."
Barr expressed disappointment on her Facebook page, saying: "Be sure to avoid Kath's Devine Cakes if you support marriage equality."
The business did not respond to request for comment.
Under New Zealand's Human Rights Act, it is illegal to refuse to provide goods or services to a person because of their sexual orientation.
The Human Rights Commission's chief legal adviser Janet Anderson-Bidois said anyone who believed they had been discriminated against because of their sexuality could make a complaint to the Commission, and it would be carefully considered.
The Commission would not comment on invididual complaints it received, she said.
A similar case in the United States went all the way to the Supreme Court after a gay couple, Charlie Craig and Dave Mullins, complained of discrimination when baker Jack Phillips refused to bake them a wedding cake.
The court sided with Phillips, but did not go as far as creating an exemption for businesses to refuse service to gay customers.
