The force of the blast broke windows in several buildings nearby, witnesses said.
The front of the 4WD embassy vehicle was partially damaged.
There was no immediate claim of responsibility for the suicide blast.
Ali Shah Paktiawal, the Kabul police chief, said: "A suicide bomber on a bicycle blew himself up. Three others were wounded, so the total number of casualties in this incident is five."
A German foreign ministry said: "The sole occupant of the vehicle, an Afghan employee of the embassy, was injured."
The latest attack to hit the capital came after a car bomb exploded outside the US embassy on Thursday, killing four Afghans and wounding 20 others. The Taliban claimed responsibility for the attack.
Violence has jumped sharply this year in Afghanistan where the Taliban, ousted in a US-led invasion, have regrouped since 2005.
More than 4,000 people, over a quarter of them civilians, have been killed so far in 2008 and the fighters have extended the scope and size of their attacks.