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The explosion happened in the suburb of Nyanya, close to a motor park where at least 70 people died in a bomb blast on 14 April.
Witnesses said the explosion targeted a police checkpoint near a bus station.
No group has claimed responsibility for Thursday's attack. The Islamist militant group Boko Haram said it was behind the fatal explosion last month.
The BBC's Will Ross in Abuja says Nyanya is a religiously mixed area and it is not clear why the area has been targeted.
Charles Osueke, who was in the area at the time of the blast, told the BBC that it was just 200 meters away from the 14 April explosion.
"People in the crowd were saying that a man parked his car, walked away and the next thing they know, the car blew up," he said. "There were policemen around when this explosion happened and they didn't manage to stop it," he added.
The head of Nigeria's Emergency Management Agency, Abbas Idriss, told the BBC that 19 people were killed in the blast and 60 others were injured.