A spokesman for the Zabul governor said the troops were part of Nato's US-led International Security Assistance Force (ISAF) and had stopped on the road to defuse a bomb.
"ISAF had to defuse a roadside bomb near a bridge when a small vehicle approached. ISAF told them to stop, fired a warning shot, then shot at the car," Mohammad Jan Rasul Yar, the spokesman, said.
Eyewitnesses said that the troops, were carrying out house-to-house searches in a village, opened fire first without firing warning shots.
Nick Carter, the ISAF regional commander, said that the military was investigating the allegations but gave no further details.
Friday’s incident is the latest in a long list of civilians mistakenly killed by US-led troops fighting the Taliban.
It comes just weeks after US troops opened fire on a bus in the southern city of Kandahar, the Taliban's spiritual capital, killing four civilians and sparking angry public protests.
It also comes one day after the French military admitted that its troops accidentally killed four children in eastern Afghanistan on April 6 in a missile attack.