Badakhshan province governor Shah Waliullah Adeeb said more than 2,000 people were missing after a hill collapsed on the village of Hobo Barik after days of heavy rain.
He said the landslide had buried some 300 homes in the area – about a third of all houses there.
Ari Gaitanis, from the UN Assistance Mission in Afghanistan, said at least 350 people had died in the landslide.
He said the UN was working with authorities in the area to rescue people still trapped.
Mr Adeeb said rescue crews were working but didn’t have enough equipment, and he appealed for shovels.
“It’s physically impossible right now,” the governor said. “We don’t have enough shovels; we need more machinery.”
He said officials had evacuated a nearby village over concerns about further landslides.
Provincial police chief Faziluddin Hayar said the landslide happened about 1pm yesterday.
Badakhshan province, nestled in the Hindu Kush and Pamir mountain ranges and bordering China, is one of the most remote in the country.
The area has seen few attacks from insurgents following the 2001 United States-led invasion of Afghanistan.
Afghans living in the rugged mountains of northern Afghanistan are used to landslides and avalanches.
In February 2010, more than 170 people were killed in an avalanche at the 3,800-metre-high Salang Pass, which is the major route through the Hindu Kush mountains that connects the capital to the north.