At least five people including 4 personnel of the National Directorate of Security were feared dead.
The strike marked the first suicide attack perpetrated by the Taliban in Kabul since a three-day ceasefire declared in mid-June on the occasion of Eid al-Fitr.
"The investigation is ongoing into the attack and more details will be shared soon", Stanekzai said.
Before this on Sunday, in a suicide bombing attack near the Kabul International Airport, 23 people were killed and over 100 people were wounded.
Responsibility for the attack claimed by the Taliban.
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The Tuesday rocket attacks injured seven, no one has still claimed responsibility for it and Kabul security bodies have not explained the issue yet.
The attacker was "most likely" driving a vehicle carrying explosives, Stanikzai added.
The last major one took place on July 22 near an worldwide airport in Kabul, minutes after the motorcade of Afghan Vice-President Abdul Rashid Dostum left the area.
This comes as the anti-government armed militant groups have been attempting to increase attacks in the key provinces and cities of the country including capital Kabul during the recent months.