The strike, near Kabul airport, killed 10 members of one family, including six children, relatives have told the BBC.
The US military said it was targeting a vehicle carrying at least one person associated with the Afghan branch of the Islamic State group.
The US was assessing and investigating reports of civilian deaths, it added.
American commanders said there were "significant secondary explosions" after the drone strike - implying there were explosives at the scene - which may have harmed people nearby.
