UN spokesman Manoel de Almeida e Silva said, “Two or three RPGs were fired at the office at about 3 am. There were no casualties. An investigation is ongoing.”
No staff were in the office when it was attacked early on Friday morning and the damage was minor, he said.
The attack was the latest on an international humanitarian agency in the south, which has been racked by a bloody insurgency by Taliban guerrillas and their allies since US-led forces overthrew the Kabul government in late 2001.
Friday’s attack came after gunmen shot dead the head of the Afghan government’s refugee department in Kandahar province and two of his bodyguards on Tuesday.
“It’s one more security incident following many that we have seen,” Silva said. “We don’t know what is behind this one.”
Mohammad Mader Farhad, a spokesman for the UN High Commissioner for Refugees, said a guard house outside the UNHCR compound was damaged.
Police returned fire and the attackers fled, he said.
The Taliban and their allies have declared a holy war against US-led foreign forces in Afghanistan and consider foreign and local aid workers a legitimate target for attack.
At least 33 foreign and local humanitarian workers have been killed in attacks since the beginning of last year, severely disrupting essential aid and reconstruction work and hampering preparations for elections due to be held in September.
Recent attacks have included the killing of three foreigners and two Afghans from aid group Medecins Sans Frontieres in the northwestern province of Badghis on 2 June, and the killing of 11 Chinese working on a World Bank-funded road project in the northern province of Kunduz on 10 June.
Those attacks raised concerns that Islamic guerrillas, who have generally confined their activities to southern and eastern areas bordering Pakistan, have extended their insurgency to previously peaceful provinces.