The incident happened in the Chahar Dara district of Kunduz province Wednesday when German troops came under attack and retaliated with gunfire, provincial police chief Abdul Rahman Sayedkhili said.
“German troops patrolling Chahar Dara district opened fire on civilian houses yesterday afternoon," Sayedhkhili told news agency AFP. "One woman was killed and another was injured as a result."
A spokesman for German troops in Kunduz, Lieutenant Colonel Klaus Geier, said he could not confirm the death but added that an investigation has been launched.
The incident is the latest to highlight the long-sensitive issue of civilian casualties caused by international troops in Afghanistan.
The deaths of nine children in an air strike last week drew a public apology from the US commander of foreign troops in Afghanistan, General David Petraeus, but this was rejected by President Hamid Karzai.
A UN report said Wednesday that Afghan civilian deaths in the war increased 15 percent last year, adding that insurgents were responsible for three-quarters of all the killings.
There are just under 5,000 German troops serving in Afghanistan, according to the NATO-led International Security Assistance Force (ISAF).