The kidnapping, the first such reported incident since the UN began to reduce its troop numbers in Darfur, comes just days after Washington lifted a 20-year-old trade embargo on Khartoum.
The Swiss foreign ministry told AFP in Geneva in an email that it was "aware of the case of a Swiss woman kidnapped in Sudan (Darfur)".
"Our local representatives are in contact with the local authorities," it said, adding that the case was being investigated.
The foreign ministry did not provide any details on the identity of the abducted woman or the circumstances surrounding her kidnapping.
The UN's top aid official in Sudan, Marta Ruedas, also confirmed the abduction to AFP.
The Swiss national had lived in Sudan for many years and was "abducted by unidentified armed perpetrators near her residence in the Agricultural Research Centre area of El Fashir late last evening," Saturday, Ruedas told AFP.
"She is not a UN staff member, but she has long collaborated with the UN on a number of initiatives."
Ruedas said the aid worker has been actively involved in humanitarian work in El Fashir, the capital of North Darfur state.
"We certainly hope that this is able to be resolved positively," Ruedas said.
The Sudanese government has not confirmed or officially commented on the incident.
But social media reports indicated the abducted woman had been working for a Swiss non-governmental organization providing aid to children.
The kidnapping came despite repeated claims by Sudanese officials that Darfur -- a region the size of France -- was now safe as the long-running conflict there had ended.
But several aid workers in Darfur had expressed concerns about their safety following the decision to withdraw some UN forces from the region.
Aid workers working in Darfur are often escorted to remote areas by UN peacekeeping troops, and they feared that their security would be comprised following the downsizing of the forces.
Just weeks ago Unamid, a joint African Union and the United Nations peacekeeping force, began reducing the number of its troops in the region, citing a fall in violence there.
The UN force had been deployed after a brutal conflict erupted in Darfur in 2003, which the UN says has killed about 300,000 people and displaced more than 2.5 million.
The conflict erupted after ethnic minority rebels took up arms against Sudanese President Omar al-Bashir's Arab-dominated government.
They accused Khartoum of marginalizing the Darfur region economically and politically.
Most of the displaced live in camps, after escaping fighting between government forces and rebels.
The latest abduction adds to an already lengthy list of foreign and Sudanese aid workers who have been kidnapped in the region in recent years.
Earlier this year three UN refugee agency workers were abducted by armed men in West Darfur state. The workers, two Nepalese and a Sudanese, were later released.
Sunday's incident also comes days after Washington lifted its two decades-old trade embargo on Khartoum.
Although the embargo was imposed for Khartoum's alleged support for Islamist militant groups, Washington had argued that the conflict in Darfur was a key factor in maintaining the sanctions all these years.
Sudanese officials, including Bashir, have repeatedly claimed that the conflict in Darfur is over.
But experts say that militias in search of resources often turn on each other in the region, and sometimes against the government.
Khartoum had in recent years insisted that UN peacekeepers leave the region, saying the conflict there had ended.