A woman, who drowned was an employee at a local hospital, was also drowned, according to the news agency.
"The accident was caused by engine failure halfway across because of a strong current," it said.
The victims' bodies have not yet been found, SUNA added.
Villagers in the region rely on wooden boats to cross the Nile .
“All the families (in the area) are in mourning,” a witness said.
Sudan suffers monsoon rains which regularly last from June to November and cause the Nile and its tributaries to overflow. The Nile is an important transport route for people and goods in the African nation.