What caused the building to collapse was not immediately apparent, and the police are yet to comment.
Construction workers close by helped to remove the roof of the building to aid rescue attempts.
Poor quality materials used in construction and negligible building standards in Nigeria are often blamed for such collapses.
Buildings are often made with blocks of sand and cement scavenged from the ocean. Rain can subsequently cause degradation of these materials.
At least three people died in July 2008 when a four-storey shopping centre in Abuja, the capital, collapsed.
In 2006, 28 people were killed when another four-storey construction, with a restaurant, bar and shops, fell down in Lagos.