Mpho Tutu van Furth practised as a vicar from January 2004 until she married Marceline van Furth, an atheist, in December 2015.
The former Archbishop of South Africa's daughter was previously married to a man and the couple had two children. Marceline van Furth was also married to a man and has two children.
The Anglican Church in South Africa currently says that "holy matrimony is the lifelong and exclusive union between one man and one woman."
It does not permit clergy to enter same-sex marriages, and Mpho Tutu van Furth's decision meant she had to leave the priesthood.
Desmond Tutu has been a vocal campaigner against discrimination towards gay people, and has publicly supported gay clergy who do not remain celibate.
Mpho Tutu van Furth told the BBC: "I knew when I married Marceline that there was a chance that I would have to give up my licence.
"It was incredibly sad for me. A few years ago I celebrated the Eucharist with my father and so to now be in a position where I can't serve at the altar with him - I was surprised by how much it hurt.
"I think it has saddened him [Desmond] as well. It is has saddened him in as much as this is where the Church is now.
"What is so absolute that we cannot pass beyond this point?
"I have to think of all of the people for whom the choice was: I can be a priest or I can be with the person I love, and I don't get to have both."