Hundreds of homes were buried under mud and rocks when a section of a mountain collapsed following torrential rain.
Rescuers have reached the area and are searching for survivors.
Much of north and east Afghanistan has been hit by heavy rain in recent days, and some 150 people have died in flooding.
“The number of deceased has increased to 350 and significant displacement is expected,” the UN mission in Afghanistan said in a statement.
“The UN Office for the Co-ordination of Humanitarian Affairs (OCHA) is helping… local authorities to rescue those still trapped.”
Local officials say that more than 2,000 people are missing.
About 1,000 houses were affected – 300 of them buried immediately after the side of a mountain gave way.
As it was Friday morning, a day of rest in Afghanistan, people were at home and whole families were lost under tonnes of mud.
Badakhshan is in the most remote and mountainous part of the country, bordering Tajikistan, China and Pakistan.
Searching for survivors is a huge task, our correspondent adds.
The governor of Badakhshan province, Shah Waliullah Adeeb, told AP news agency that rescue crews did not have enough equipment and appealed for shovels.
“It’s physically impossible right now,” Shah Waliullah Adeeb said.
“We don’t have enough shovels; we need more machinery.”
Shah Waliullah Adeeb said that residents of nearby villages had been evacuated amid concerns about further landslides.
Another, smaller landslide was reported in Badakhshan on Thursday.
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