Officials say the bomb went off inside Mammy market where people were eating and drinking to celebrate New Year's Eve.
No one has claimed responsibility for the attack.
Nigerian President Goodluck Jonathan blamed the bombing on the group Boko Haram.
The group claimed responsibility for Christmas Eve bomb attacks in the central city of Jos, and for attacking several churches in the northern city of Maiduguri. More than 80 people died in those attacks.
Abuja was shaken by car bomb attacks in October. Militants from the southern oil-producing Niger Delta claimed responsibility for those blasts.