The U.S. Embassy and North Atlantic Treaty Organisation headquarters are also located in the area.
Monday's rush-hour attack occurred outside the main entrance to the security compound.
Another Interior Ministry spokesman told the AFP news agency that six civilians were killed while riding in their vehicle when the attacker, traveling on foot, detonated his bomb.
Security measures were boosted after a May 31 truck bomb attack near the German embassy in the diplomatic quarter that killed at least 150 people and wounded about 400 others.
"They were hit when they were passing the area in their Toyota sedan vehicle".More news: Kentucky woman killed by two pit bulls and husband hurt
More news: Okanagan Hockey Academy alumni to make Olympic debut in 2018
More news: Conor McGregor says he wants 'MMA next' instead of boxing
ISIS has claimed responsibility for the attack, according to CNN.
"The bomber was on foot and detonated his suicide vest on the main road", he said.
Qari Yusouf Ahmadi, a Taliban spokesman, claimed responsibility for the attack in Helmand.
Last week, a group of Islamic State militants stormed an under construction building near training facility of the NDS in Afshar area in Kabul.
The assault came to an end after forces successfully killed two attackers.