Another 14 police officers were wounded in the bomb which was detonated amid a group of security officials monitoring protests by shopkeepers.
There was no immediate claim of responsibility for the attack.
Kabul has been hit hard by terror attacks attributed to Taliban, Islamic State (IS), and other militants operating in the country.
Ministry of Public Health and Kabul Police have confirmed the casualties.
The Emergency Hospital in Kabul said in a tweet that at least 20 wounded were brought to the facility following the explosion.
I.S. say the bomber, with an explosive belt, was targetting "a gathering of Afghan intelligence and police".
As security forces arrived at the scene, a Reuters reporter saw four police vehicles carrying dead or wounded security personnel leaving the scene in an area of the city not far from the US Embassy and other foreign missions.
President Ashraf Ghani condemned the "barbaric attack" and ordered an investigation, according to a statement from the presidential palace.
Several days ago a suicide bomber killed more than 40 people at a Shi'ite cultural centre in the capital.
On Wednesday, Afghanistan's spy agency announced it had busted a 13-member IS cell in Kabul that had been hatching "a series of big terrorist attacks" in the city.