A spokesman for the UN mission in Kabul, Don McNorton, said: "We are aware of an incident in our Mazar office, we are currently working to ascertain all the facts."
Afghanistan had condemned the "disrespectful and abhorrent" burning of the Koran by evangelical preacher Pastor Wayne Sapp in a Florida church, calling it an effort to incite tension between religions.
President Hamid Karzai called on the United States to bring those responsible for the burning of the Islamic holy book on March 21 to justice.
Sapp set light to a Koran under the supervision of Terry Jones, who last year drew condemnation over his aborted plan to burn a pile of the holy books to mark the anniversary of the September 11, 2001 attacks.
Jones cancelled his plans under enormous pressure from world leaders including US President Barack Obama, but the mere threat to burn the Muslim holy book sparked large protests in Afghanistan, where the UN and aid groups warned that civilians and aid workers in the country could be killed if the pastor went ahead.
Afghanistan is a deeply devout Islamic country where even rumours that the Koran has been insulted can result in deadly violence.
In January last year seven tribesmen were killed when Afghan security forces opened fire at demonstrations sparked by the alleged desecration of a Koran by US troops in the southern province of Helmand, a hotbed of insurgency.
The demonstrators were trying to overrun NATO bases and police facilities when they were fired on.
A subsequent investigation by NATO and Afghan authorities found that no Koran had been torched during an operation by the Western troops.
Afghan officials say the Taliban, the main militant group fighting the insurgency, fabricate stories that Western troops have insulted the religion in order to whip up anti-US sentiment.
These attempts are often successful.
In May 2008, a foreign soldier serving under NATO command was killed during demonstrations by Afghan tribesmen against the shooting of a Koran by a US soldier in Iraq. Two Afghan protesters were also killed when the shooting broke out.
Friday's attack followed a protest march led by religious clerics and attended by around 200 in Kabul on Friday against the Koran burning and plans announced by Karzai in February for possible permanent US bases in Afghanistan.
The demonstrators, who left from mosques in downtown Kabul after Friday prayers, burned a US flag and stamped on it, shouting "Death to America".
