sentenced to death on Thursday, judicial officials said.
According to the Sudanese officials, 26-year-old Meriam Ibrahim, whose father was Muslim, was convicted on Sunday and given four days to repent and escape death. She was sentenced after that grace period expired, the officials said, speaking on condition of anonymity in line with regulations.
The sentencing drew condemnation from Western embassies in the Sudanese capital, Khartoum, and international rights groups, including Amnesty International.
The court in Khartoum also ordered Ibrahim be given 100 lashes for committing "zena" — an Arabic word for illegitimate sex — for having sexual relations with a non-Muslim man.
The couple married in 2011 and have a child, born 18 months ago. Under Sudanese law, Ibrahim's marriage to a non-Muslim is regarded as void.
Ibrahim can appeal her death sentence as well as the 100 lashes.
As in many Muslim nations, Muslim women in Sudan are prohibited from marrying non-Muslims, though Muslim men can marry outside their faith. By law, children must follow their father's religion.
Amnesty International said Ibrahim's conviction and death sentence were "truly abhorrent."
"The fact that a woman has been sentenced to death for her religious choice, and to flogging for being married to a man of an allegedly different religion is appalling and abhorrent," the London-based rights group said in a statement. "Adultery and apostasy are acts which should not be considered crimes at all."
The group also called for Ibrahim's immediate and unconditional release.
Sudan introduced Islamic Sharia laws in the early 1980s, a move that contributed to the resumption of an insurgency in the mostly animist and Christian south of Sudan. An earlier round of civil war lasted 17 years and ended in 1972. The south seceded in 2011 to become the world's newest nation, South Sudan.
Sudan's current ruler, Omar Bashir, is an Islamist who seized power in a 1989 coup.