The blast destroyed a huge portion of the five-storey building that houses 400 employees of the UN.
Police said 18 people died in the blast while eight others were injured. Among the dead was an unidentified foreign national besides two women, Daily Times newspaper reported.
Witnesses said the blast happened when a car rammed into the front of the building after crashing through two security barriers. The building is the UN's main office in Nigeria, where 26 humanitarian and development agencies are based.
The rescue work was on at the site and fire fighters and police officers cordoned off the area.
Cranes were deployed to remove the debris so as to ensure that no-one is trapped under.
UN Secretary-General Ban Ki-moon strongly condemned the attack, saying "this was an assault on those who devote their lives to helping others."
"We condemn this terrible act utterly," he said, adding the UN did not have exact casualty figures "but they are likely to be considerable."
An eyewitness said some 300 people could be trapped in the building as its first, second and third floors, including the reception area, were heavily damaged by the blast.
"The UN building is located at Area 1 Abuja and I could see emergency and security agencies scrambling to evacuate the building," he told PTI.
Police spokesman Yemi Ajayi said police had dispatched its men to provide security and to help the relief workers.
No group has so far claimed responsibility for the attack, but it is suspected that this could be be the handiwork of radical Islamist sect, Boko Haram, the newspaper said.
Nigeria's Minister of State for Foreign Affairs Viola Onwuliri told the BBC she had visited the building and seen "the shock on people's faces".
"This is not an attack on Nigeria but on the global community," she said. "An attack on the world."
According to rescuers, the workers at the basement of the building were among those worst affected by the blast.
"All the people in the basement were killed. Their bodies are littered all over the place. I saw about 5 dead bodies," Ocilaje Michael, a UN staff member at the building, was quoted as saying.
Oil-rich Nigeria's population is 150 million and the country is split between a largely Christian south and Muslim north.
Nigeria has faced an increasing threat from Boko Haram, which wants to impose the strict Shariah law on the country.
The sect is responsible for assassinations and bombings, including the June car bombing of the national headquarters of the federal police that killed at least two people.
