The air strike in the province's Baraki Barak district came after five civilians were killed and six others injured in a similar NATO attack in Afghanistan in December 2014.
Referring to the latest incident, District Governor Mohammad Rahim Amin said that the targeted checkpoint was "not a suspicious area", and that the strike was likely a mistake, due to bad coordination.
"The Afghan flag was waving at the checkpoint in Baraki Barak when the Americans launched their attack," he said.
A US military official, said that he was aware of the Monday morning's incident, which he said is "under investigation."
Although the US-led NATO forces wrapped up their combat mission in Afghanistan in December 2014, about 10,000 international troops are still in place in Afghanistan to train and advise Afghan forces; the coalition troops' fighting role is limited to special operations.
As for the latest "friendly fire", it occurred as Taliban militants intensified attacks on government and foreign targets during their summer offensive; ending the hostilities was high on the agenda of last week's talks between Afghan officials and Taliban leaders, who agreed to meet again in the coming weeks.