German Defence Ministry spokesman Thomas Raabe said the incident, which killed three civilians and injured others, was under investigation.
The police chief of Kunduz, Abdul Rahman Aqtash told news agency dpa that the dead included a woman and two children. He added that four other children were injured in the attack.
Speaking at a government press conference in Berlin, Raabe said two civilian vehicles which neared a checkpoint manned by the Afghan police and German ISAF (International Security Assistance Force) soldiers in Kunduz in northern Afghanistan on Thursday night failed to stop despite a signal to do so.
"The security forces opened fire ... Three people were killed, all civilians," he said. "The incident is currently being investigated."
Raabe said the probe was seeking to determine whether German soldiers had fired the fatal shots and whether the civilian vehicles contained weapons or explosives.
On Wednesday an IED (improvised explosive device) exploded next to an eight-vehicle German convoy patrolling the outskirts of Kunduz where the German military has its base, killing one German soldier and injuring three.
The killing came a week after 10 French soldiers died and 21 were wounded in the most lethal ground battle for international soldiers who arrived in Afghanistan in 2001 to topple the Taliban regime and root out extremists.
Most of the attacks are concentrated in southern and eastern Afghanistan, but there has also been scattered violence in the country's north and west. Germany has some 3,500 troops stationed in northern Afghanistan as part of the NATO military alliance's International Security Assistance Force.