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.
Fears over security
Charles Osueke, who was in the area at the time of the blast, told the BBC that it was just 200m (650ft) 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.
“I’m worried about our security here. After the last explosion the president said he would increase security,” Mr Osueke added.
“There were policemen around when this explosion happened and they didn’t manage to stop it.”
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.
Campaign of violence
Most of Boko Haram’s attacks have been in the north-east of Nigeria.
But the bombing on 14 April raised fears that the militants could be trying to expand their area of operation.
In a video message after that attack, the group’s leader Abubakar Shekau said: “We are in your city but you don’t know where we are.”
The latest attack comes just days before Abuja is set to host the World Economic Forum on Africa after becoming the continent’s biggest economy last month.
Insecurity will be a major concern with several world leaders, including Chinese Premier Li Keqiang, due to attend the event.
Correspondents say the blast comes at a terrible time for Nigeria, which is also dealing with the abduction of 230 schoolgirls that happened hours after the previous Nyanya attack.
Boko Haram’s fighters have killed more than 1,500 civilians in three states in north-east Nigeria this year.
The group has hit Abuja several times before, including an attack on the United Nations building in 2011.
But before 14 April, there had not been an attack in the capital for two years.
Boko Haram, whose name means “Western education is forbidden” in the local Hausa language, has been waging a campaign of gun and bomb attacks since 2009.