The UN said that it had closed its offices in Pakistan since the attack, although no specific threat had been received.
Security camera footage broadcast on local TV showed the bomber walking through a door into what appears to be the main building carrying a half-metre long cylindrical object in one hand.
Seconds later, a bright flash fills the screen.
Officials said that the assailant, who was in his twenties, was dressed as a paramilitary officer and had asked a guard to use the building's bathroom, before detonating his explosives in the lobby.
Visitors to UN buildings in Islamabad are usually frisked or pass through a metal detector and the blast has raised questions over security at the WFP office.
Kamal Hyder, Al Jazeera's correspondent in Islamabad, said: "This building is heavily fortified. On the outside it is completely bunkered with bomb proof walls around it.
"According to the reports we are getting there were over 50 people inside the building.
"We can see that the front door has been taken out, the windows are shattered. But there appears to be no structural damage. Some smoke is still billowing out [of the building].
"We were told that many of the wounded were immediately rushed off in private vehicles, some belonging to the WFP itself. Then ambulances arrived."
Ban Ki-moon, the UN secretary-general, condemned the bombing.
"This is a terrible tragedy for the UN and for the whole humanitarian community in Pakistan," he said in a statement issued in Geneva where he is on a two-day visit.
The attack could hamper the work of WFP and other aid agencies assisting Pakistanis displaced by army offensives against al-Qaeda and the Taliban in their strongholds close to the Afghan border.