Authorities said at least 15 people had been rescued from the rubble of the building that collapsed Tuesday afternoon.
Government officials did not immediately say what caused the collapse in a poor neighbourhood of the sprawling city of about 21 million people. Rescue efforts continued overnight and into Wednesday morning.
An Associated Press photographer at the scene saw the body of one adult pulled from the rubble. It was not clear how many people were living in the building.
Hundreds of people gathered at the scene where rescue workers and heavy machinery were sifting through the rubble.
Building collapses are not uncommon in the West African powerhouse where corruption is rampant and infrastructure often poor.
Lagos, Nigeria's commercial hub, is said to be Africa's largest city.