"A suicide attacker has detonated himself... close to a number of police who were trying to provide security for an ongoing protest," deputy interior ministry spokesman Nasrat Rahimi told AFP.
Health ministry spokesman Wahid Majroh told AFP that 11 bodies had been taken to hospitals around the city along with 25 wounded.
Majroh added that the toll could rise.
A security source who spoke to AFP on the condition of anonymity said 20 people had been killed and 20 wounded in the attack, but that higher toll could not be immediately confirmed.
The deadly assault comes a week after more than 40 people were killed and dozens more wounded in a suicide blast claimed by the Islamic State group that targeted Shiites in Kabul.
The capital 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.
Last week's assault came days after a suicide bomber killed six civilians in a Christmas Day attack near an Afghan intelligence agency compound in the city, which was also claimed by IS.
Security in Kabul has been ramped up since May 31 when a massive truck bomb ripped through the diplomatic quarter, killing some 150 people and wounding around 400 others -- mostly civilians. No group has yet claimed that attack.
Despite the increased security measures militants continue to carry out attacks.
On Wednesday Afghanistan's spy agency announced it had busted a 13-member IS cell in Kabul that had been planning to carry out "a series of big terrorist attacks" in the city.
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