Her family are extremely worried about her welfare, saying she is not being given access to medical treatment in jail.
One relative said: "We are concerned for her wellbeing. It is not very safe for her to be in the prison with dangerous criminals."
According to human rights organisation Christian Solidarity Worldwide, Ibrahim was born in western Sudan to Muslim father and a Christian mother. Her father left when she was 6, so her mother raised her as a Christian. She married Daniel Wani, a Christian from southern Sudan who has United States citizenship, in 2011.
The charity added that three witnesses from western Sudan had travelled to the hearing to testify that Ibrahim had always been a Christian, but were prevented from giving evidence.
It is understood that the death sentence will not be enacted for two years after she has given birth, but that the punishment of 100 lashes could be carried out as soon as her baby is born. Ibrahim's lawyers are intending to launch an appeal, which could take several months.
Governments across the world condemned the move. Mark Simmonds, Britain's Minister for Africa, said he was "truly appalled" at the outcome of the case.
"This barbaric sentence highlights the stark divide between the practices of the Sudanese courts and the country's international human rights obligations," he said.
"The UK opposes the use of the death penalty in all circumstances and urges the Government of Sudan to join what is a clear global trend to abolition."
Ahead of the sentencing, the British embassy in Khartoum issued a joint statement with the US, Canada and the Netherlands expressing its "deep concern" about the 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, a right which is enshrined in international human rights law as well as in Sudan's own 2005 Interim Constitution," the statement said.
Manar Idriss, Amnesty International's Sudan researcher, said: "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. Adultery and apostasy are acts which should not be considered crimes at all. It is flagrant breach of international human rights law."
Sudan has a majority Muslim population and has been governed by Islamic law since 1983, but extreme punishments other than flogging are rare. Apostasy, the crime of abandoning or criticising Islam, is punishable by death in several Muslim-majority countries.
Ahmed Bilal Osman, Sudan's Information Minister, told the AFP news agency: "It's not only Sudan. In Saudi Arabia, in all the Muslim countries, it is not allowed at all for a Muslim to change his religion."
If the death sentence is carried out, Ibrahim will become the first person to be executed for apostasy under the country's 1991 penal code.
- Independent