© UnknownWhen the fail is so strong, one facepalm is not enough
They were killed in the early hours of Thursday in the Charkh district of Logar province.
Nato confirmed the "unfortunate incident" and said it was investigating the circumstances behind the attack.
Correspondents say it is likely to anger President Hamid Karzai, who has been deeply critical of international air strikes that have killed civilians.
Afghan defence ministry spokesman Zahir Azimi said on his Twitter account that five soldiers had been killed and eight others wounded in the overnight attack.
District governor Khalilullah Kamal, who has visited the scene, said the strike was carried out by a US drone.
"The post is totally destroyed," he told the AFP news agency. "The Americans used to be in that post, but since they left the ANA [Afghan army] took over."
In a statement, the Nato-led security mission Isaf said it values "the strong relationship with our Afghan partners, and we will determine what actions will be taken to ensure incidents like this do not happen again".
Most foreign troops are scheduled to leave Afghanistan by the end of the year.
President Karzai has refused to sign a security deal with the United States that would allow a reduced presence of international troops to remain in Afghanistan beyond that date.
Comment: Yet another Drone Killing! You'd think with the increase in technology, they would be less prone to error? Apparently not, the trigger happy U.S. Drone Gamers just couldn't resist.
This is likely to send some serious ripples through the international community as the U.S, EU, and NATO are trying to project a holier-than-thou image as they try to strong arm Russia over America's FAILED Coup d'Etat in the Ukraine.
I can't see how these yahoos could have any credibility left.