Fakori Behishti, a member of parliament from Bamyan province, and his son were wounded in the blast, an official with the parliament's security department said.
There was no immediate claim of responsibility for the attack, which destroyed the vehicle in which Behishti was travelling, badly damaged other vehicles and shattered the windows of nearby shops.
Last week, another member of parliament was targeted by a suicide bomber who killed seven people. The member of parliament survived.