The New York Times said officials have not confirmed the number of dead or wounded, but Khaama Press indicated the total was 35 people.
The explosion occurred at one of the gates of the National Directorate of Security and could be heard for miles, the Times reported. The attack was followed by sporadic gunfire.
The Taliban claimed responsibility.
"We targeted a very important NDS installation in Kabul in the heart of the city while foreign advisers where there," Taliban spokesman Zabiullah Mujahid told the Times from an undisclosed location.
Qais Noori said the blast heavily damaged the shop where he works.
"I was in the shop when suddenly I heard a massive explosion and the roof collapsed," he told the Times. "The owner told us all to go home."
Khaama Press also reported an explosion in the village of Sar-Shakhlo in Uruzgan province Wednesday killed at least two Afghan security personnel and wounded two others.
An official said the explosion occurred while Afghan security forces were working to defuse a roadside bomb.