"We don't know who took them. There are so many splinter groups in the area you'd only be guessing," O'Shea told the Reuters news agency.
"The local police force are in charge of trying to track them down. We have never had a kidnapping before. We are just hoping and praying that we can get them back."
There was no immediate claim of responsibility.
The incident marks the third kidnapping of foreign aid workers in Darfur since March, when armed men seized four members of the Doctors Without Borders medical aid group.
They were freed a few days later.
In April, a French national and a Canadian aid worker were seized in southern Darfur and released three weeks later.
Clashes between ethnic minority fighters and the Arab-dominated government and its allies in the western Sudanese region of Darfur has been ongoing since 2003.
The UN says the fighting has killed up to 300,000 people and displaced an estimated 2.7 million, but Khartoum disputes the figures, saying that only 10,000 people have died in the conflict.