The bomb blast happened late on Thursday night on a busy road across from the same bus station where an explosion on 14 April killed at least 75 people.
The Islamist militant group Boko Haram has claimed responsibility.
Abuja is to host the World Economic Forum on Africa next week and the government has dedicated 6,000 police to guard the event.
The summit attracts world leaders, policy-makers, philanthropists and business figures to discuss prospects for economic growth across the continent.
Last week, Nigerian president Goodluck Jonathan assured delegates they would be safe.
The explosion happened in a working-class suburb a 15-minute drive from Nigeria’s presidential villa and the hotel venue of the conference.
Police Superintendent Frank Mba told reporters the death toll was up to 19 with as many wounded being treated in hospitals.
Six cars were destroyed in the blast, he said.
Witnesses said a car laden with explosives drove close to the checkpoint and a man jumped out and ran as it blew up.
A deafening explosion was followed by smaller ones as other cars caught fire and fuel tanks erupted, they said.
The attacks are a major embarrassment that undermine government and military assurances that Boko Haram had been contained in a north-east corner of the country. Two unexploded bombs were found at the scene, according to a security official.
Boko Haram means “Western education is sinful”. The group wants to create an Islamic state in Nigeria, which it claims would halt crippling corruption that keeps 70 per cent of the people in Africa’s richest nation impoverished.
Hours after the 14 April car bombing, which wounded at least 141 people, Boko Haram militants kidnapped more than 300 teenage girls at a school in the remote north-east, which is their stronghold.
Officials said 53 have escaped but 276 remain captive.
Reports this week indicated some of the girls have been forced into “marriage” with their abductors, who paid a nominal bride price equivalent to £7.
Other reports that also could not be verified said some have been taken across borders, to Chad, Cameroon and to an island in Lake Chad. The reports come from parents and politicians who are in touch with villagers who have seen the girls with their abductors.