The strike took place on Monday morning in Logar province's district of Baraki Barak, about 50km east of Kabul.
"The strike was likely a mistake, due to bad coordination," district governor Mohammad Rahim Amin was quoted as saying by Al-Jazeera.
A similar NATO air strike in the area in December last year killed five civilians and wounded six others.
Taliban insurgents are active in the area.
The NATO-led International Security Assistance Force (ISAF) Sunday formally ended its 13-year-old combat mission in Afghanistan in December, 2014, but a residual force remains for training and counter-terrorism operations.
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Security in Logar has deteriorated in recent months as the Taliban stepped up their attacks on Afghan soldiers and security forces, trying to spread their footprint across the country and take control of some remote regions.