According to Sputnik, the terrorist group claimed responsibility for the attack via one of its websites.
The suicide attacker hit Kabul’s Shash Darak area on Saturday, killing at least three people and injuring six others.
The area lies close to the NATO’s headquarters and not far from the American Embassy.
Afghan Interior Ministry spokesman Najib Danish said the casualty count could rise.
Afghanistan has seen rampant instability since the 2001 invasion of the country by a United States-led NATO coalition, which ousted a Taliban regime at the time. The Taliban then launched a militancy, targeting foreign and Afghan forces as well as civilians.
The Takfiri Daesh terrorist group is a more recent phenomenon in Afghanistan. But it has managed to establish a foothold in the already-conflict-ridden country.