President Goodluck Jonathan blamed the blast on an Islamist group that claimed responsibility for bombings on Christmas Eve in central Nigeria that killed at least 80 people.
The explosion occurred at Mami market, a busy area where people congregate to socialise on the edge of the Sani Abacha army barracks.
Boko Haram, a radical sect that wants Islamic law throughout Nigeria, said it was behind the bombings in Jos on 24 December, which also wounded more than 100.
The police say the group is to blame for a series of shootings and blasts in northern Nigeria in the past week that come just four months before a presidential election that could heighten religious and ethnic rivalries in the oil exporting nation.
"There are four dead and at least 13 injured," police spokesman Moshood Jimoh said.
"The scene has been cordoned off by security agents and an investigation has commenced. Security has been tightened around the city."
A worker at the military medical centre in the barracks said at least 11 people had been killed and many more casualties were being taken to other hospitals in Abuja.
"Sixteen victims were brought into the hospital, four were dead but the other 12 are in a stable condition," Udofia Enefion, director general at Asokoro Hospital, said.
One witness said he was approaching the market to join the New Year's Eve celebrations when he heard the blast. "People ran in different directions. There were scores of bodies - dead and wounded." Eric, a market regular said.
Later President Jonathan said: "Tonight, evil people determined to turn the joys of fellow Nigerians to ashes detonated a bomb at a barracks market in the federal capital.
"Basking in their nefarious success in Jos on Christmas Eve, they have once again knifed at the heartstrings of a nation."
On Thursday, police arrested Bunu Wasili, a 65-year-old businessman, accused of financing the radical group.