Rescue crews were trying to reach the remote areas of Badakhshan province where a number of houses were reported to have been destroyed on Monday, said Shams Ul-Rahman, deputy provincial governor.
Between 6-9 feet (2-3 meters) of snow have fallen in the area, making roads to the provincial capital of Faizabad impassable.
“We have reports of at least 14 dead and several others injured,” Ul-Rahman said, adding that several other people were missing.
Avalanches present a constant danger in many parts of Afghanistan during the winter.
In February 2010, an avalanche killed at least 171 people near the 12,700-foot (3,800-meter) high Salang Pass, a major route through the Hindu Kush mountains that connects the Afghan capital of Kabul to the north of the country.
Meanwhile, Afghan President Hamid Karzai urged the Taleban to allow teams conducting a polio vaccination campaign access to areas under the insurgents’ control.
Afghanistan is one of just three nations where polio remains endemic. The two others are Nigeria and neighboring Pakistan.
“Whoever prevents the polio vaccination is the enemy of our children’s future,” Karzai said in a statement.
Last year, the government registered 80 new cases of polio, most of them in the restive southern provinces. That figure was three times higher than the total for 2010.
The polio virus, which usually infects children in unsanitary conditions, attacks the central nervous system, sometimes causing paralysis, muscular atrophy, deformation and, in some cases, death.
“Karzai called on the armed opposition to the government to allow the medical teams to vaccinate the children and rescue them from polio,” the government statement said.
Karzai said that although millions of Afghan children had been inoculated in successive vaccination campaigns, many remained outside the reach of health officials because of the security situation in areas in the south and along the border with Pakistan.
Karzai’s appeal came just days after another country in the region, India, celebrated a full year since its last reported case of polio, a major victory in a global eradication effort.