The jeep was damaged but its armour plating prevented anyone inside from being hurt and the vehicle made it safely back to base at Kunduz, a spokeswoman for the bank said.
The KfW is involved in reconstruction work in northern Afghanistan, where Berlin has around 3,500 troops serving under the NATO-led International Security Assistance Force.
A suicide bombing targeting the German military 35 kilometers (20 miles) south of the city on Wednesday left three soldiers wounded, two of them seriously, according to the German military.
"We don't yet know how things will turn out," military doctor Sebastian Hentsch at the Bundeswehr hospital in Koblenz said on Friday. "The biggest problem is the lung injuries."
On Thursday, Afghan authorities also rescued a German-Afghan businessman kidnapped nearly two weeks ago in Kabul from captors who had been demanding ransom.