Police spotted the speeding car and opened fire, but hit a nearby taxi and killed its driver.
Julia Gross, a spokeswoman for Germany's Foreign Ministry, confirmed the reports.
"A German citizen was abducted in Kabul. We must assume it was a kidnapping."
"The Foreign Ministry's crisis team is engaged and working toward a solution in close cooperation with Afghan officials," Gross said in Berlin.
Ulf Baumann, a spokesman for Ora International, said the 31-year-old woman and her husband, also a German, worked for his organisation in Kabul since September 2006.
Baumann did not disclose the woman's name or her husband's.
Abduction fears have risen after 23 South Koreans and two Germans were taken hostage in separate incidents in July in central Afghanistan.
One of the German men was shot dead while the other remains in captivity.
Taliban fighters killed two of the South Koreans and released two others after talks with South Korean officials.
Qari Yousef Ahmadi, a Taliban spokesman, said the group's demands for the release of the remaining 19 South Koreans remain the same - a swap for Taliban prisoners, which the Afghan government has ruled out.
Separately on Saturday, a suicide bomber detonated an explosive-packed car west of Kandahar, killing 15 people including three women and two children, police said.