Mariam Yahya Ibrahim, 27, was arrested for converting to Christianity from Islam, and has been held with her 20-month-old son in Sudan. She is eight months pregnant.
Western embassies appealed for the woman to be let go on compassionate grounds, and asked Sudan to respect religious freedom and her right to choose her faith.
But the Judge said that after giving the woman three days to covert back to Islam, she had chosen not to and therefore must face death by hanging.
The mother has also been sentenced to 100 lashes for adultery, due to her marrying a Christian man.
East Africa's Sudan is ruled by Sharia law - which outlaws converting religions from Islam.
Human rights organisations have slammed the ruling, with Amnesty International saying that the sentences were 'abhorrent.'
They added: 'Adultery and apostasy are acts which should not be considered crimes at all. It is flagrant breach of international human rights law.'
Britain, the U.S., and Canada are among the nations who have expressed concern over the woman's case - with representatives from these embassies appearing in court to hear the ruling.