The Dana Air flight was heading from Lagos to Abuja, Nigerian Civil Aviation Authority head Harold Denuren told AP news agency.
He was quoted elsewhere saying he did not believe any of the 153 people on board had survived.
The crash took place in a neighbourhood just outside the airport, AP quoted federal emergency management as saying.
It said emergency personnel were on their way to the scene.
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.