The spokesman added that the family filed a lawsuit against the German Foreign Ministry after it rejected a request for help to bring the wife back to Germany with her children from a Kurdish-controlled area in northern Syria.
Germany, like other Western countries, has a problem dealing with its citizens who have joined mercenaries in Syria, where hundreds of them are being held in northern and eastern Syria.
The unidentified gunman left for Syria with his wife and two daughters, now 7 and 8 years old in 2014, and his wife gave birth to a third child in Syria two years ago, according to German sources.
A spokesman for the German Foreign Ministry said the government was considering the verdict and might appeal it to a higher court. A family representative's lawyer did not respond to a request for comment.
German intelligence officials say more than 1,000 Germans have gone to fight in Syria and Iraq, where mercenaries have been in control of vast tracts of land.
One-third of those returned to Germany and another two-thirds are believed to have been killed, while the remaining third are believed to remain in Iraq and Syria, officials said.