The accident took place Sunday while the victims were fleeing the town of Malakal where fighting has broken out between the South Sudanese government and rebel forces, BBC quoted an army spokesperson as saying.
"The reports we have are of between 200 to 300 people, including women and children. The boat was overloaded," the spokesperson said, adding that women and children were among the victims.
"They all drowned. They were fleeing the fighting that broke out again in Malakal."
The boat was overloaded.
More than 350,000 people have been displaced by the fighting between the South Sudanese government and rebel forces, according to the UN.
Rebels say they have captured Malakal, which is the gateway to the oilfields of the Upper Nile region.
However, this has been denied by the army, which maintains that the rebels had been pushed back after heavy fighting in the city.
Malakal is located on the banks of the White Nile - just north of its confluence with the Sobat River.
Thousands of civilians have been trying to escape the clashes by crossing the river, but many say they simply cannot afford to pay for a boat, according to the BBC.
Some 9,000 civilians have recently arrived at a UN base in Malakal, almost doubling the number of people seeking shelter there.