Health Ministry officials confirmed another 20 people were wounded in the blast, which took place in a heavily-guarded area housing several diplomatic missions and the offices of international organizations.
ISIS claimed the bombing in a brief statement on its Aamaq news agency, without specifying the target.
The attack took place about 500 meters (yards) from the American Embassy, but there were no reports of foreigners killed or wounded.
Gen. Dawlat Waziri, spokesman for the Defense Ministry, said the bomber was on foot. The police promptly cordoned off the area of the attack.
Kabul police spokesman has said that the suicide bomber was a 12-year-old child who blew up his explosive vest at the 14th street of Wazir Akbar Khan.