Another 14 police officers were wounded in the bomb which was detonated amid a group of security officials monitoring protests by shopkeepers.
The Islamic State (IS) militant group claimed responsibility through its Amaq news agency, although it provided no evidence to back up the claim.
Afghan police had launched an operation on Wednesday in two Kabul city districts to arrest the sellers of alcohol and drugs - both of which are illegal substances in Afghanistan - and made 11 arrests.
The number of casualties has been confirmed by Ministry of Public Health and Kabul Police, reported TOLO News.
Several days ago a suicide bomber killed more than 40 people at a Shi'ite cultural centre in the capital.
This is the first such bombing in Kabul this year.
In December alone IS claimed three attacks that killed dozens of civilians.
Kabul has become one of the deadliest places in war-torn Afghanistan for civilians in recent months, as the Taliban step up their attacks and IS seeks to expand its presence in the country.
I.S. say the bomber, with an explosive belt, was targetting "a gathering of Afghan intelligence and police".
Despite the increased security measures, militants continue to plan and carry out devastating attacks.
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