The children survived but emerged from the car spattered with blood, screaming and traumatised. The soldiers tended to them and brought them to hospital.
The incident happened in Tal Afar, near Mosul, in northern Iraq, late on Tuesday.
According to the US military, soldiers with the 1st Battalion, 5th Infantry Stryker Brigade Combat Team of the 25th Infantry Division out of Fort Lewis, Washington, fired on the car when it failed to stop and came towards soldiers, despite warning shots, during a dusk patrol.
The US forces' press service said the military extended its condolences for the incident, but added that "the military must take appropriate action against possible threats" because of the prevalence of car bombs.
The incident was witnessed by Chris Hondros, a photographer, who recorded it in a series of dramatic pictures. They show how troops shot dead the driver and one passenger - husband and wife, apparently, but unnamed in the photograph captions.
The five children in the rear of the car survived, with only one being slightly injured by a bullet. The military said it was investigating what happened.