"The accident occurred around 7.45pm yesterday in (the neighbourhood of) Festac Town when a wooden boat with some 20 passengers capsized," Ibrahim Farinloye of the National Emergency Management Agency told AFP.
"We have recovered 13 bodies, including two children, from the water while six others have been rescued," he said, adding that the boat had a capacity of just 12 people.
The boat was used to ferry people across a small river within the Festac Town neighbourhood.
The Lagos government has aggressively tried to promote water travel around the city of 20 million people to reduce choking traffic, especially between the so-called mainland where most people live and the commercial and business hubs on the city's islands.
A few ferry services are considered safe with well-maintained boats, but most are ramshackle operations, often in decaying motor-powered canoes run by untrained pilots.