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.
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