Reverend Canon Mpho Tutu-van Furth can no longer preside at Holy Communion, weddings, baptisms or funerals after handing in her licence because the church does not recognise gay marriage.
She said her father, the retired archbishop and celebrated anti-apartheid campaigner, was "sad but not surprised" at the news.
"The canon (law) of the South African Church states that marriage is between one man and one woman," Tutu-van Furth said in an email.
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