The bomb went off on Friday after a suicide bomber forced his way through two security gates and rammed his car into the building, blowing out the first two floors.
At least 18 people died in the attack, according to an AP survey of morgues at four major Abuja hospitals.
The building is located in the same neighbourhood as the US embassy and other diplomatic posts in Abuja.
An Islamist group blamed for a series of attacks in the country claimed responsibility for the bombing.
Al Jazeera’s Yvonne Ndege, reporting from the scene of the attack, said:”This is one of the heavily guarded buildings in Nigeria – it houses international diplomats and foreign workers.
“This entire area has been cordoned off. There are military men and security services in the area, security has been heighted within the entire city. Road blocks have been erected, they want to make sure there are no further attacks here in Abuja.”
In recent months, the country has faced an increasing threat from Boko Haram, which has been waging war against the Nigerian government, our correspondent said.
The group has carried out assassinations and bombings, including the June car bombing of the national headquarters of Nigeria’s federal police that killed at least two people.
“The Islamist sect has in the past attacked symbols of authority so people are asking if this a change of tactic – with international people working for the betterment of Nigeria [being attacked].
“Some people are saying the attackers are using Boko Haram as a front.”
The headquarters, known as UN House, had offices for about 400 employees working for 26 UN humanitarian and development agencies.
UN Secretary-General Ban Ki-moon called the car bombing “an assault on those who devote their lives to helping others.”
“We condemn this terrible act, utterly … We do not yet have precise casualty figures but they are likely to be considerable. A number of people are dead; many more are wounded,” he said.
Ban said he was sending his deputy, Asha-Rose Migiro, to Nigeria immediately to meet officials in Abuja.