An emergency management official said more than 40 people had been freed.
It was not known how many students had been in a primary school located on the building's top floor.
Officials of the Lagos State Emergency Management Agency (LASEMA) and other rescue official are now at the scene. "That is the secondary level but the most important thing right now is to save lives and I just appeal to people that they should give us the chance to save more lives", he said.
Emergency rescuers trawled through the wreckage of the disaster, trying to save those still trapped in the building which housed, among other uses, a nursery school. TVC Correspondent, Theophilus Elamah reports.
About two dozen people have been rescued so far, said freelancer Anna Cunningham, reporting from the scene for CBC News.
There were residential apartments below the school, Cunningham reported.
The building was in the Ita-faji area of Lagos island, the original heart of the lagoon city before it expanded onto the mainland.
SCHIFF: Pelosi 'Absolutely Right' Not to Pursue Partisan Impeachment
She said the House would never even consider the separate bill limiting future declarations by presidents, including Trump. There are also court challenges asserting Congress, not the president, decides how taxpayer money is spent.
As residents of the area trooped to the site of the crumbled building, an unnamed distressed lady who reportedly took her aunt's child to the school earlier in the morning was spotted weeping bitterly after the tragic incident.
"HURIWA also called for the forensic audits of all public building assets including malls; stadia and places of worship to safeguard the lives of millions of Nigerians in Lagos".
Presidency Muhammadu Buhari said in a statement he was "extremely saddened" by the building collapse.
Onlookers crowded around the area in the densely populated neighborhood in Lagos, Nigeria's commercial capital.
In September 2014, 116 people died when a six-storey building collapsed in Lagos during a service given by a celebrity televangelist.
Building collapses are frequent in Nigeria, where regulations are poorly enforced and construction materials are often substandard.