The kidnappings were the latest in a wave that has hit Darfur, which is in the throes of a seven-year revolt, in the past year.
"One American lady and two Sudanese men were abducted," Sudan's state minister for humanitarian affairs, Abdel Bagi Jaylani, told Reuters.
"I am appealing to the international NGOs (non-governmental organizations) to restrict the movement of the expatriate staff," he added.
A UN spokesman in Khartoum, Sam Hendricks, said eight armed men carjacked a two-vehicle convoy and took three of the aid workers with them just outside Nyala, the capital of South Darfur state.
Four South Africans from the UN-African Union peacekeeping mission were kidnapped in Nyala last month but released after the Sudanese government struck a deal with their captors.
The US embassy in Khartoum declined to comment.
The United Nations estimates some 300,000 people have died in the humanitarian crisis caused by a counter-insurgency campaign in western Sudan which also drove 2 million people from their homes. Sudan says the number of deaths is far lower.
A faltering peace process has been set back by clashes between Sudan's army and Darfur's rebel Justice and Equality Movement (JEM).
The movement on Tuesday released 44 army prisoners for what it said was humanitarian reasons but warned of more attacks.
The International Committee of the Red Cross used UN World Food Program helicopters to transport the prisoners to el-Fasher, North Darfur, it said in a statement.
But spokesman Al-Tahir Al-Feki said that did not mean the movement would rejoin the peace process, which it left after accusing the government of attacking its positions.
"The peace process is now more in jeopardy than ever before. Their (Khartoum's) intention was to annihilate us but they failed," he said.
