One official said 10 people had been "critically injured". However, an official quoted by AFP news agency reports "a number of dead".
While Islamist group Boko Haram has attacked Abuja before, its insurgency has mostly focused on the north-east.
Maiduguri, the capital of Borno state, is where the militants first based its campaign to carve out an Islamist state in 2009.
Friday`s explosions in two suburbs of Abuja happened "almost simultaneously" at about 22:30 (21:30 GMT), a spokesman for the National Emergency Management Agency told AFP.
"There are a number of dead but we can`t say anything about numbers now," Manzo Ezekiel said.
The explosives, he continued, appeared to be "the same kind of explosives used in the insurgency" in the north-east.
Two separate attacks at a bus station in Nyanya killed 90 people last year.
Some 17,000 people are said to have been killed since Boko Haram began its insurgency and attacks by the group have intensified since Muhammadu Buhari became president in May, vowing to defeat the insurgents.
This year, security forces have managed to reclaim most of the territory captured by Boko Haram fighters and freed a number of people kidnapped by the militant group.
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