"She gave birth to a girl today," said the diplomat, who is familiar with the case of Meriam Yahia Ibrahim Ishag, 27.
"The mother and the baby seem to be doing OK," said the diplomat who asked for anonymity.
But he said: "It's a cruel treatment to be in such a situation."
The case of Ishag has sparked global outrage since a Khartoum-area court sentenced her to death on May 15.
Born to a Muslim father, she was convicted under the Islamic sharia law that has been in force in Sudan since 1983 and outlaws conversions on pain of death.
"To give birth in jail... is certainly not the best place, for physical and psychological reasons," the diplomat said.
Ishag's husband, who is Christian, did not respond to telephone calls on Tuesday.
Human rights activists have said Ishag is being held at a women's prison in Khartoum's twin city Omdurman with her first child, a 20-month-old son.
"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 said as he sentenced Ishag, addressing her by her father's Muslim name, Adraf Al-Hadi Mohammed Abdullah.
Khalifa also sentenced her to 100 lashes for "adultery". Under Sudan's interpretation of sharia, a Muslim woman cannot marry a non-Muslim man and any such relationship is regarded as adulterous.
"I am a Christian and I never committed apostasy," Ishag calmly told the judge before he passed sentence.
The diplomat said of the case: "For the image of Sudan, it's certainly no good."
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