The blast shook the Emab Plaza, not far from the country's parliament, at 4pm local time (0100 Thursday AEST), the National Emergency Management Agency (NEMA) said, as shoppers were buying groceries ahead of the country's World Cup match against Argentina, which kicked-off an hour later.
"The casualty figure for now is 21 persons dead, 17 injured," national police spokesman Frank Mba said, adding that an arrest had been made.
Senior government spokesman Mike Omeri confirmed that the blast was the result of "a bomb attack".
Rescue teams were deployed to the scene and evacuated the victims from the area, NEMA spokesman Manzo Ezekiel told AFP.
"The explosion struck at peak business time," he said, adding that the area was busy at the time of the blast and that 40 cars had been destroyed.
The blast, at the entrance to the mall, was powerful enough to blow out windows in buildings on the opposite side of the street, an AFP correspondent on the scene in the immediate aftermath said.
An employee of the nearby Newcastle Hotel in the Wuse II area of the city, who did not want to be named, said she clearly heard the explosion.
Nigerian emergency officials work on the scene of a bomb blast in Abuja, Nigeria, 25 June 2014. (AAP)
Soldiers and police cordoned off the area and firefighters were at the scene, as thick smoke billowed into the sky, an AFP reporter said.
Boko Haram which sparked worldwide outrage by kidnapping more than 200 schoolgirls in April, has attacked Nigeria's capital twice in the last 10 weeks.
A car bombing killed 75 people at the Nyanya bus terminal on the outskirts of the city on April 14 while a copycat bombing at the same spot on May 1 left 19 people dead.
