Flooding caused by torrential rains struck a village in Nangarhar Province late on Friday, district governor Naimatullah Noorzai told AFP.
He said 16 people, including 15 children aged between one and five years, and a woman were killed.
Four children were also injured and dozens of houses were destroyed, Noorzai said.
A relief operation was under way to help affected families, with the disaster striking as the country celebrates the Muslim holiday of Eid al-Adha.
A spokesman to the governor of Nangarhar Province confirmed the death toll.
Torrential downpours, flash floods and harsh winter weather kill scores of people annually in Afghanistan.
Many poorly built homes, mostly in rural areas, are at risk of collapse during the rains in the impoverished country.