Meriam Yehya Ibrahim, 27, who was born to a Muslim father but brought up a Christian by her mother, was convicted on Sunday and given three days to recant her faith or face a possible death sentence.
"We gave you three days to recant but you insist on not returning to Islam. I sentence you to be hanged," Judge Abbas Mohammed Al-Khalifa told Mrs Ibrahim, addressing her by her father's name, Adraf Al-Hadi Mohammed Abdullah.
Mrs Ibrahim also faces a sentence of flogging for adultery on the grounds that her marriage to a Christian man from South Sudan is considered void under Islamic law. She will be given 100 lashes. Because her father was Muslim, she was considered by the court to be the same.
Mrs Ibrahim told the judge: "I am a Christian and I never committed apostasy."
Amnesty International said Mrs Ibrahim was eight months pregnant and in detention with her 20-month-old son. A spokesman said: "The fact that a woman could be sentenced to death for her religious choice and to flogging for being married to a man of an allegedly different religion is abhorrent and should never be even considered."
The sentence has been condemned by the international community. In a joint statement, the embassies of Britain, the United States, Canada and the Netherlands expressed "deep concern" over her case.
"We call upon the government of Sudan to respect the right to freedom of religion, including one's right to change one's faith or beliefs," they said.