Abdul Marouf Rasekh, a spokesman for the governor of Badakhshan province, said the outbreak began three days ago and was restricted to one town that has been quarantined.
When it first appeared in the mountainous village of Chappa in the Darayen district, Rasekh said it infected 850 people but quickly spread until the quarantine was put in place.
"The village has been quarantined and they are all being treated," he said, adding that "treating such diseases is not easy."
He said that 36 of the most serious cases have been taken to a hospital in the provincial capital of Faizabad and that the sole death so far was an 18-year old woman.
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Afghanistan has had cholera outbreaks in the past but they are not common. Typhoid and other intestinal diseases and parasites are far more common but not as deadly if left untreated.
The World Health Organization says cholera is virulent but mortality rates are low if treated quickly.