The air plane struck a two-storey building and burst into flames, witnesses said.
The head of the Nigerian Civil Aviation Authority said he doubted anyone could have survived the crash. Thousands of onlookers were drawn to the crash site.
Rescue services pulled at least one body from the rubble and were searching for survivors, AP news agency said.
The plane crashed in the densely populated Iju neighbourhood, just north of the airport, Lagos State police spokesman Joseph Jaiyeoba told AFP.
The commercial DC-10 plane was flying from the Nigerian capital, Abuja, to Lagos when the crash took place.
There were chaotic scenes as onlookers and emergency services rushed to the crash site.
At the crash site, reporters saw plane wreckage scattered around and the body of the plane lodged into an apartment building.
Firefighters tried to put out the smouldering flames of the jet engine as black smoke billowed.
Several charred corpses could be seen in the rubble, reported AP.
The weather at the time of the crash was overcast – but there were none of the storms that regularly strike the city, says the BBC’s East Africa correspondent Will Ross.
Last month a Similar Dana Air plane – possibly the same one – developed a technical problem and was forced to make an emergency landing in Lagos, our correspondent adds.
Nigeria, like many African countries, has a poor air safety record, though some efforts have been made to improve it since a spate of airline disasters in 2005.