The payment was made in order to prevent further unrest as a result of last Thursday's shooting, the paper reported, though without source attribution. It did not say how much money was paid.
A defence ministry spokesperson confirmed the report on Wednesday afternoon, saying Defence Minister Franz Josef Jung had arranged the compensation during a surprise visit to Afghanistan on Tuesday to pay his respects to the relatives. The payment has insured that revenge is off the table, but the payment was not an admission of guilt.
Prosecutors in Potsdam outside Berlin have reportedly launched proceedings against one of the German soldiers involved for suspected manslaughter. They could not be reached for comment.
German and NATO forces said last week that the three civilians were killed after both German and Afghan troops opened fire on a vehicle that had failed to stop at a checkpoint even after warning shots had been fired. The German defence ministry denied a report in Monday's Financial Times Deutschland newspaper that the German troops had failed to follow the rules of engagement.
It was one of a recent string of incidents that analysts say are damaging the reputation of the almost 70,000 international troops as well as the Afghan government, which need the backing of the local population if they want to beat a Taliban-led insurgency.
On Monday NATO-led troops accidentally killed three Afghan children in artillery fire in eastern Afghanistan, the force said, while the same day Afghans alleged that international troops had killed four people, including two young boys and their father, in an early morning raid in Kabul.
The incident last week involving the German soldiers came a day after an improvised explosive device went off near an eight-vehicle German convoy, killing one German soldier and injuring three. The death brought the the death toll of international soldiers to 187 for the year.