The boat left on Friday from the remote town of Oron, in Cross Rivers state, across the Gulf of Guinea and was heading to Gabon, in central Africa, traders said.
David Akate, head of Cross Rivers emergency services, confirmed the incident and said all the passengers on-board died.
He added that the two known survivors were a young boy and a woman who had clung to a gas cylinder and were rescued by fishermen.
"They are mostly Igbo traders from the southeast who headed to Oron to board the wooden boat because it was cheaper," said Ikechukwu Egwu, a marine transporter in the area.
Boat accidents are relatively common in Africa, where safety standards are poor. As many as 138 people died when an overloaded boat carrying passengers and goods capsized in rough water on a river in Democratic Republic of Congo in 2010.
Some 35 people taking this route from Nigeria to Gabon died after their boat sunk off the coast of Cameroon in 2008.