Another 52 people were injured in the blast, according to Ministry of Public Health spokesman Wahid Majroh.
A spokesman for Kabul city police, Basir Mojahid, said the attacker was trying to reach the capital's Sakhi shrine, where people had gathered to celebrate the Persian new year, known as Nowruz.
Before reaching the shrine, the attacker was identified by security forces and blew himself up in front of Kabul University, Mojahid said. The blast happened about 12:40 p.m. local time (4 a.m. ET).
ISIS claimed responsibility for the blast in a statement, saying an attacker it named as Abu Talha al-Peshawri had detonated his explosive vest among "polytheists" gathering to celebrate Nowruz.
The US Ambassador to Afghanistan, John R. Bass, condemned the attack as "shameful" on his official Twitter account and said the United States was committed to working with the Afghan authorities "to secure peace in the year ahead."
A series of attacks in the capital this year had already fueled doubts over the Afghan authorities' ability to keep people safe.
The group has not publicly responded to the proposal.