Boko Haram has killed thousands and made the group the biggest threat to security in Africa's top oil producer, is increasingly targeting the civilian population.
The bomb went off at around 6 pm in a busy market area in Ajilari-Gomari near the city's airport, two witnesses and a police source said.
"I am at the scene now, it is very bad," local resident Ismaila Abdulraman told Reuters by telephone.
"Many men, women and children died. The fire service are on the ground now and they are bringing corpses of people and trying to put out the fire at the scene," Abdulraman added, saying he had already seen 10 bodies.
The final death toll was likely to be higher because dozens of people were trapped in the rubble, the witnesses said.
There was no immediate claim of responsibility for the bombing, but Boko Haram only communicates occasionally through Internet videos, days or weeks after attacks.
The military and police did not immediately respond to requests for official comment.
President Goodluck Jonathan started an intensified military push to end Boko Haram's four-and-a-half year insurgency almost a year ago but the bloodshed has not diminished. He is expected to run in a closely contested election next year.
The violence has been largely contained to Nigeria's remote northeastern rural areas on the borders with Cameroon and Niger, far from commercial hubs such as Lagos and Abuja, and from the southern oil fields. The attack in the northeast's biggest city marks a setback for Jonathan's military campaign.