The woman and a male colleague were seized by armed men from a compound in the west Darfur town of Zalingei in late August, the latest in a new wave of abductions in the area.
Sources close to the kidnappers told officials the woman fell ill a few days ago, the spokesman for the peacekeeping UNAMID force, Noureddine Mezni, told Reuters.
"She has not been feeling well for a few days. We are trying our best to send them some medicine," said Mezni.
"They were both healthy before they were abducted. But being held captive for two weeks in the bush is not going to be good for your health." He said the male peacekeeper was in a "better condition", declining to give details about the woman’s health.
Mezni said the force was concerned about the situation. "Our number one priority is to secure the release of our two colleagues."
UNAMID has not released the names, ages or nationalities of the kidnapped pair, who are members of the force’s civilian staff. Sources from the United Nations and Sudan’s government have said the woman is from Zimbabwe and the man from Nigeria.
Khartoum has blamed the kidnapping on bandits seeking a ransom, and said the abductors have already contacted UNAMID to try and negotiate a payment.
Kidnappers have seized four groups of foreigners in Darfur since March, and one international aid worker a few miles over the border with neighbouring Chad.
Two women working for Irish aid groups GOAL, one from Ireland, the other Ugandan, are still in captivity more than two months after they were taken from the north Darfur town of Kutum. Other workers were released unharmed after negotiation, with both Khartoum and their employers insisting no ransoms were paid.
Kidnappings of foreigners in Darfur were almost unheard of before March.
Aid groups say they have faced increased hostility and threats since the International Criminal Court issued an arrest warrant that month for Sudan’s President Omar Hassan al-Bashir, to face charges that he masterminded war crimes in Darfur.
The Darfur conflict surged in 2003 after mostly non-Arab rebels took up arms against Sudan’s government, accusing it of neglecting the region. Khartoum mobilised troops and mostly Arab militias to crush the uprising, unleashing a wave of violence that Washington has called genocide. Khartoum dismisses the accusation. Reuters