Ballarat-based minister Steve North reportedly told the couple he would no longer marry them and that they could not hold their ceremony at the Ebenezer St John's Presbyterian Church, according to Fairfax.
His decision came after a pro-same-sex marriage Facebook post by the bride-to-be, The Age reported on Friday.
Victorian Premier Daniel Andrews said he thought "we would have moved beyond that sort of prejudice".
But the prime minister says "churches are entitled to marry or not marry whom they please".
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"That is part of religious freedom. My own church, the Catholic Church, will not marry someone who has married before," Mr Turnbull told reporters in Canberra.
Minister Steven North, of Ebenezer St John's in Ballarat, is claimed to have told the couple he would not be able to officiate the wedding just days after the bride-to-be made a Facebook comment supporting the yes ballot.
"I know it's something not everyone will agree on and that's fine but this is what I stand for and frankly it doesn't effect [sic] my relationship with [my partner] one bit," the 26-year-old bride reportedly wrote.
Mr North reportedly followed up the meeting with a letter to the couple, revealed by Fairfax, to explain the decision to cancel the wedding because it opposed the teachings of the Presbyterian Church of Australia.
"After the pre-marital counselling that you attended and the sermons delivered at Ebenezer on this subject, you must surely appreciate that your commitment to same-sex marriage opposes the teaching of Christ Jesus and the scriptural position practiced by the Presbyterian Church of Australia and by me," Mr North wrote, according to Fairfax.
"This conflict of views has practical consequences in relation to your upcoming wedding."
The couple did not wish to be named for privacy reasons.
SBS World News contacted Steven North, Ebenezer St John's Church and the Presbyterian Church of Australia for comment.
The Presbyterian Church of Victoria was not able provide a comment either.
