The accident happened as a group of from the Shegarab-1 camp in the eastern state of Kassala tried to cross the Atbara river yesterday evening.
"There was an attempt to smuggle some of these asylum-seekers out of the camp and they were being transported on four rickety, small fishing boats," said Mohammed Adar, the UNHCR representative in Sudan.
One of the boats sank and "eight bodies have been found and two are still missing," he said, adding that another 10 people swam to safety and returned to the camp.
Adar said the United Nations had not verified the nationality of the dead but said the government had sent a team to investigate.
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Their intended destination was unknown, but eastern Sudan has a significant refugee population, the majority Eritreans fleeing a military regime at home.
Nearly 110,000 Eritreans currently live throughout Sudan.
The Shegarab-1 camp is jointly run by the Sudanese government and the UN and houses 15,000 people, mostly asylum-seekers.