"It occurred at around 10 a.m. local time (0530 GMT) when a suicide bomber after shooting dead a security guard broke into the ministry building and detonated himself on the first floor killing five and injuring 15 more," the statement said.
"One security guard, three employees of the ministry were among the deaths," it said.
It added that "those injured includes women and children."
"It is a cowardly attack and the Taliban once again remind us of their complete disregard for and hostility toward Afghanistan's noble cultural heritage and traditional values," it further noted.
Moreover, both Afghan government and NATO-led International Security Assistance Force (ISAF) condemned the deadly attack and expressed condolences to the victims and their families.
Afghan President Hamid Karzai, who is on a visit to Turkey attending the World Economic Forum on Europe and Asia, described in a statement released by his office that the attack was another attempt by the enemies of Afghanistan to undermine peace and security.
Taliban militants fighting Afghan government has claimed responsibility for the attack.
Zabihullah Mujahid who claims to speak for the militants told media outlets from unknown locations via telephone that a fighter named Naqibullah after opening fire outside the building broke into the building and blew himself up causing huge casualties.
Mujahid added that there were three attackers carrying out the assault but he did not say about the fate of the remaining two.
The radical Taliban outfit carried out a deadly suicide car blast targeting the Indian Embassy on July 7, leaving over 50 including two Indian diplomats dead and 141 more injured, mostly civilians.
Spiraling conflicts and Taliban-linked insurgency have claimed lives of around 5,000 people with over 1,500 civilians so far this year in Afghanistan while Taliban insurgents have vowed to intensify assaults against the interests of Afghan government and international troops before the coming winter.