Ibrahim Farinloye, spokesman for the National Emergency Management Agency's south-west region, said a three-storey building came down at around 10:00am local time.
Meanwhile, some residents of Itafaji area of Lagos Island reportedly pelted Governor Akinwunmi Ambode with sachets of water as he left the venue of the collapsed building.
Adeshina Tiamiyu, general manager of the Lagos State Emergency Management Agency, said that the agency had recorded one death so far in the disaster, and had rescued almost 50 people.
But they had also recovered "more than four dead bodies", Mr Tiamiyu said without giving an exact figure.
Mr. Kunle Awobodu, 1st Vice President, Nigerian Institute of Building NIOB, and the immediate past President of Building Collapse Prevention Guild BCPG, while reacting to yesterday's collapsed building in Ita Faji Street, Lagos Island, said "From our findings which revealed over 1000 structures were distressed, we had also recommended that those structures should be earmarked for demolition in Lagos Island".
The building was a mixture of residential apartments and classrooms, according to local media. All we are trying to do is to scale up this rescue operation.
It is not clear whether the collapsed building failed to meet safety standards.
An AFP reporter at the scene saw at least eight people pulled from the wreckage, including a small boy with blood on his face. Dust-covered children, some moving and some still, were rushed to waiting ambulances throughout the afternoon and evening.
Rescue efforts underway after Lagos school collapse
"HURIWA wondered why Lagos has persistently become a hub for substandard buildings going by the numerous cases of building collapse just as the Rights group condemned the snail speed dispensation of justice in Lagos with specific reference to cases of collapse buildings even as it blamed judicial corruption for this ugly trend". They cheered as the child was lifted out.
Adeshida, whose younger sister was the mother of the children, said she was angry because people had complained about the building for the last 12 years.
Rescue efforts were expected to continue through the night Wednesday.
It is characterised by its Afro-Brazilian architecture, a style brought over by thousands of freed slaves who headed back home after decades working the plantations in Brazil.
Building collapses are tragically common in Nigeria, where building regulations are routinely flouted.
Emergency and rescue teams are now at the scene of the incident, Pulse has learnt.
An inquiry found the building had been built illegally and had structural flaws.
In December 2016, at least 60 people were killed by the collapse of a church roof in the city of Uyo, east of the country.