Local media report the sentence would not be carried out for two years after she has given birth.
Sudan has a majority Muslim population, which is governed by Islamic law. It rules that apostasy - the abandonment of one's religious faith - is a crime.
Amnesty International said the woman, Meriam Yehya Ibrahim Ishag, was raised as an Orthodox Christian, her mother's religion, because her father, a Muslim, was reportedly absent during her childhood.
In court, the judge addressed her by her Muslim name, Adraf Al-Hadi Mohammed Abdullah.
She was also convicted of adultery on the grounds that her marriage to a Christian man from South Sudan was void under Sudan's version of Islamic law, which says Muslim women cannot marry non-Muslims. For this the judge sentenced her to 100 lashes. This punishment will reportedly be carried out when she has recovered from giving birth.
The woman's lawyer has said that he will appeal the verdict. Amnesty International has condemned the verdict. Also on Tuesday, the embassies of the United States, Canada, the United Kingdom and the Netherlands issued a joint statement expressing "deep concern" about the case and urging Sudan to respect the right to freedom of religion, AFP says. The woman was arrested and charged with adultery in August 2013, and the court added the charge of apostasy in February 2014 when she said she was a Christian and not a Muslim, Amnesty said.