The attack, which was carried out in Spin Kalay square in PD5 of the city, targeted the vehicle of Haji Khan Mohammad Wardak, a member of parliament from Kabul, according to the statement.
Wardak was injured in the attack, the statement noted.
No group has so far claimed responsibility for the attack.
Since 2001 when the United States invaded Afghanistan, over 100,000 people have been killed in the war, including more than 4,000 ISAF soldiers and civilian contractors, more than 62,000 Afghan national security forces, 31,000 civilians and even more Taliban members.