State-run Radio Nigeria said the death toll could rise as high as 135 after the boat, which was carrying 150 people and large quantities of farm produce, hit a submerged object.
"It happened last night. It is feared that more than 30 people must have died in the accident," a police spokesman said on Thursday by telephone from the Anambra state capital, Awka.
"Our primary concern now is to see how many people can be rescued alive."
The boat was travelling from the Ogidi district of Anambra state to a large market town, Onitsha, located on the banks of the river.
Nigeria's waterways and roads are some of the most dangerous in the world, a situation made worse by the lack of emergency services. Police routinely blame the large number of deaths on overloading, speeding and poor maintenance.
Last week, newspapers said at least 20 people drowned when their boat capsized near a remote village in southwest Nigeria, although police said only five died.