Naguibullah Hashemi, a member of the provincial council told the Middle East News Agency the incident took place at around 9:30 am Monday near the house of Atta-ullah Faizani, provincial council member in Chehelsotoon area of Kabul city.
The blast occurred when Mr Faizani was heading towards work, he said.
Meanwhile, witnesses in the area say that a number of civilians were also injured in the attack.
The blast came just hours after a suicide bomber hit a minibus carrying Nepalese security contractors, in which 14 people were killed and nine others wounded in Pul-e-Charkhi area of Kabul.
There was no immediate claim of responsibility for the second blast.