The IS-linked Amaq news agency said two fighters "detonated explosive belts at a gathering of Shia" in Kabul.
The attack in Deh Mazang square targeted thousands from the Shia Hazara minority who were protesting over a new power line, saying its route bypasses provinces where many of them live.
The Taliban have condemned the attack.
Spokesperson Zabiullah Mujaheed sent an e-mail to the media saying they were not behind it.
Self-styled IS has a presence in eastern Afghanistan but has not previously admitted carrying out assaults in the capital.
