The airstrike took place in the Shigal district of the Kunar Province, an area with a heavy Taliban presence.
Afghan officials say the 10 dead civilians were from two local families.
District governor Abdul Zahir said three Taliban commanders, including a notorious Al Qaeda-linked militant leader called Shahpoor, were also killed in the raid.
He said it was not clear if the owner of the targeted house was a member of the Taliban or a civilian, but the Taliban were visiting when the home was attacked.
NATO would not confirm whether any civilian deaths took place, but said it was investigating.
"We take every allegation of civilian casualties very seriously," a spokesman said.
The incident is likely to raise tension between the US and the Afghan government.
Civilian casualties caused by NATO forces are a highly sensitive issue and are regularly condemned by Afghan president Hamid Karzai.
Mr Karzai has often said the war against terrorism should not be fought in Afghan villages.
The airstrike came within hours of US president Barack Obama's declaration that he would be withdrawing 34,000 US troops from Afghanistan by the end of this year.
Other NATO nations, which have about 37,000 troops in total in Afghanistan, will also withdraw them in stages before the end of 2014.