Abdul Rab, a 44-year-old Afghan medical doctor, and his driver, Abdul Hafiz, left Kabul for Kunduz in the far north on Tuesday, but failed to arrive at their destination, the organization said in a statement.
It said Afghan authorities found their vehicle empty in Shar-i-Kar, north of Kabul, after it reported them missing.
"We don't know whether they have been kidnapped," said Johanna Kutter, a spokesman for the Stuttgart-based organisation that specializes in health care projects for children.
KinderBerg said Rab has worked for humanitarian organizations in Afghanistan for more than 10 years.
The Taliban are waging an increasingly bloody insurgency in Afghanistan which, besides attacking security forces, includes the kidnapping of foreign nationals.
A German engineer was kidnapped by the hardline Islamist movement last year and freed in October along with five Afghans in exchange for five Taliban prisoners after being held hostage for three months. Another German hostage was shot dead by kidnappers after being seized in July.
Germany has some 3,200 troops stationed in northern Afghanistan as part of the NATO-led International Security Assistance Force.