Of the 157 children that were living in the children's home in the Ghazni province, only the youngest girls remain in the building, in two rooms where the roof is still intact, the agency said citing a report by local authorities.
The report said the children who abandoned the home do not have winter clothes.
Over the past two months, the impoverished south Asian country has experienced its coldest winter in decades, with temperatures plummeting to minus 30 degrees Centigrade (minus 22 Fahrenheit) in 17 of the country's 34 provinces.
Afghanistan's freezing weather has so far taken the lives of almost 800 people.
At least 100 people across the country have had limbs amputated due to frostbite, many of them mountain shepherds. The number of amputees continues to rise, even though the freeze is gradually easing.
Avalanches and heavy snowfall have destroyed more than 730 houses, and nearly 230,000 cattle have died in blizzards and frost.
The situation in northern provinces became so desperate last month that three Afghan girls were reportedly sold for food by their parents in separate incidents in the Herat, Kunduz and Takhar provinces. Several similar cases have been reported this month.
