The incident occurred on Sunday when a patrol of the NATO-led International Security Assistance Force (ISAF) was ambushed by Taliban militants in Naad Ali district. The coalition forces had to open retaliation fire, the alliance said.
On Sunday evening, two children were brought to the alliance's base. One of them later died, the alliance said.
Taliban militants use civilian population as human shields for their attacks, the alliance said.
U.S. President Barack Obama has said the U.S. leadership plans to double the number of U.S. troops in Afghanistan from the current 36,000 to 60,000 in the next 18 months to fight Taliban militants.