An explosion hit the popular Emab Plaza, in Wuse 2, Abuja on Wednesday killing 21 people.
A statement by Force Public Relations Officer, ACP Frank Mba, also said 17 persons were injured and 17 vehicles burnt.
Mba, who said the police was not in a hurry to de-construct the crime, did not confirm if the blast was from a car laced with bomb.
“We just want to confirm the fact that there was an explosion here (Abuja) this afternoon.
“The unfortunate incident happened at about 3.50pm….
“The casualty figure for now is 21 persons dead, 17 injured.
“There are also 17 vehicles that were burnt in the incident.
“It is also heartwarming to note that an arrest has been made and security agencies will be following up with that arrest.
“The building is still an active crime scene and it has been cordoned off.
“Investigations have already commenced.
“The police bomb disposal squad working in conjunction with other security agencies are already carrying out investigations.
“Is it a car explosion?
“We will not be in a hurry to de-construct the crime.
“It’s part of the thing that will be revealed in the ongoing investigation.
“As soon as we have that those details, we will gladly inform Nigerians,” the statement from Mba said.
A witness said the explosion occurred just as people in the area were preparing to watch a FIFA World Cup match between the Super Eagles of Nigeria and Argentina
The blast shattered windows and people could be seen fleeing the shops.
Islamist militant group Boko Haram has bombed targets across northern Nigeria in recent years.
Manzo Ezekiel, spokesman for the National Emergency Management Agency, told AFP news agency: “You can see smoke billowing from the sky. It’s a very crowded place.”
One witness told Reuters news agency that people could be seen running out of the shopping centre with blood on their clothes.
“I heard a loud blast, it shattered the windows of the shop,” Gimbya Jafaru, who was shopping nearby, said.
This is the third bomb attack on the capital city in three months.
In April, more than 70 people were killed in a bomb blast at a bus stop on the outskirts of the capital in an attack claimed by Boko Haram.
In May, a car bomb near a bus station in the suburbs killed at least 19 people and injured 60 others.
The group has hit Abuja several times before, including an attack on the United Nations national headquarters in 2011.
It has come under the international spotlight after it recently abducted more than 200 girls from a school in northern Nigeria.