Officials said it was likely people on the ground also died, but it was unknown how many, CBS News reported.
SaharaReporters.com said the twin-engine McDonnell Douglas aircraft was approaching Murtala Mohammed International Airport in Lagos, only 4 minutes short of landing, when the crash occurred. The report said Flight 9J-996, originated from Abuja.
CBS said the crash attracted a large crowd of local residents, making it difficult for ambulances to reach the scene. Some residents assisted in dragging a fire hose to the wreckage while others took photos with their cellphones.
Photos from the crash site showed people standing atop pieces of the wreckage.
The U.S. network said several charred bodies could be seen in the rubble of the building as firefighters pulled a body from the plane.
A woman told CBS she was with her children nearby when the plane went down.
"They were shouting I should leave there and look out, a plane about to land on top my head," she said. "When the plane passed, it bended. And we thought the plane was going to land, and the plane it went, it went again and it [went] down. The next thing, we just heard a sound. We noticed the plane has already crashed."
Time magazine reported that while the Nigerian civil aviation authority had not provided an official death toll, there appeared to be no survivors.
"It is unlikely anyone on board the plane survived unless there is a miracle," Tunji Oketunbi, a spokesman for Nigeria's Accident Investigation Bureau, told the U.S. news magazine.
"Thick black smoke surrounding the area and fire at the wreckage is making search and rescue efforts difficult."
An official said the jetliner hit two buildings and that surrounding homes and shops were destroyed, Time reported.
The cause of the accident was not immediately reported. Time reported an aviation official said the cockpit recorder was located and given police.
President Goodluck Jonathan declared three days of national mourning.
"President Jonathan assures air travelers in the country that every possible effort will be made to ensure that the right lessons are learned from the tragic loss of valuable lives in today's plane crash and that further measures will be put in place to boost aviation safety in the country," a statement issued by the president's office said.
The crash came the day after a Boeing 727 cargo plane en route from Lagos crashed at Ghana's international airport, killing at least 10 people.