Witnesses told Reuters news agency they saw the Dana Air plane strike the two-storey building and burst into flames.
At least 162 people were thought to be on board, but the head of the Nigerian Civil Aviation Authority said he doubted any could have survived.
The crash took place in a neighborhood just outside the airport in overcast weather, reports said.
Federal emergency personnel were said to be on their way to the scene.
There were conflicting reports as to whether the flight was arriving in Lagos from the Nigerian capital, Abuja, or was leaving Lagos bound for Abuja when the crash happened.
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.
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