Reverend Cardy wrote to ZM late yesterday telling them it was not possible to hold the finale of their Fabulous Gay Wedding competition at his Hobson St church.
The radio station is planning to arrange a church wedding for the winner of its competition on August 19 - the day legislation allowing same sex marriage comes into force.
This morning Reverend Cardy told APNZ it was the policy of the Anglican Church that the legally binding civil ceremony part of a wedding "can't be taken by an Anglican priest at this point in time".
"The doctrines of the Anglican Church unfortunately justify marriage as between a man and a woman and until we change that doctrine, which will take quite a bit of changing, that's the status quo."
Gay couples were still welcome to have a religious ceremony in an Anglican church, but had to have the civil ceremony elsewhere first, Rev Cardy said.
"That's different than for a heterosexual couple and all I can say is I'm sorry about that.
"I'm not sure what ZM are going to do but I, as an Anglican priest, can't take that civil ceremony."
Station content director Christian Boston said St Matthew's had been "incredibly supportive" of the competition but it appeared "higher powers in the church have been looking at the Anglican Church policy and have concluded that they can't marry a gay couple".
The Anglican Church statement said the organisation defines marriage as between a man and a woman.
"Within the Church, discussions are taking place about the nature of marriage and the Church's response to those who are seeking same-gender marriage. The Anglican Church seeks to be a welcoming place to all people, including the gay community, and is committed to how that can be so in practice while retaining respect for the diverse beliefs of many people in the church over this issue.
"The Anglican Church's governance structures in New Zealand are independent of the Church of England. It is not possible for the Church of England to issue orders or instructions to the New Zealand Church. Such a suggestion by ZM is incorrect and a result of a misunderstanding of church governance structures."
ZM breakfast host Polly Gillespie moved to assure competition finalists the winner would still get a church wedding.
"We are left with no alternative but to move the ceremony elsewhere, so we're on the hunt for another church.
"I feel for vicar Glynn and St Matthew's in the City, as they have been hugely supportive, I love their courage and approach to life as we know it in 2013."
Reverend Cardy announced earlier this month he would be leaving St Matthew's to lead a Presbyterian church in Remuera. The Anglican Church's stance on gay marriage had nothing to do with his decision, he said.
He was unsure whether the Presbyterian Church would allow gay marriages.