The so-called Islamic State (IS) says it is behind the attack.
All of the dead were police.
The deputy spokesperson for the ministry of interior Nasrat Rahimi told reporters in Kabul today that 13 policemen lost their lives in the attack.
The blast stripped bark from trees and shattered windows of nearby apartments, underscoring the devastating force of a single suicide bomber.
Despite increased security measures, Kabul has become one of the deadliest places for civilians in war-torn Afghanistan in recent months due to increased Taliban attacks and IS attempts to expand its influence in the country.
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Earlier it was reported that at least 15 people died in the suicide bomb attack.
The local Tolo News stated that it was a suicide attack.
IS claimed responsibility for the December 28 attack, which Afghan President Ashraf Ghani called a "crime against humanity" committed by terrorists.
The blast happened close to a group of security personnel who were carrying out an operation against illegal drugs and alcohol dealing, officials said.
On Wednesday, Afghanistan's spy agency announced it had busted a 13-member Isis cell in Kabul that had been planning to carry out "a series of big terrorist attacks" in the city.