Dr Waheed Majroh, a spokesman for the ministry of public health, said 65 people were wounded in the attack and are being treated in hospitals in the city.
He said the attacker was on foot.
Initial reports suggest the bomber attacked a crowd of hundreds of people who had gathered to celebrate the start of Nowruz, the New Year festival. Afghanistan's minority Shiites typically celebrate by visiting shrines. Instead, "he detonated his explosive on Kabul University Road, right in front of Ali Abad hospital, among the civilians who were on the way to shrine", he added.
The Islamic State claimed responsibility for this attack via its Amaq website, though both the Taliban and ISIS have carried out attacks in the capital in recent months, spreading terror and fear across Kabul. Earlier reports said the bomb was planted in a vehicle, but the city police later confirmed it was a suicide bomber. He said an investigation into the security breach is underway, and that anyone found to have neglected his duties would be punished.
During midday, a suicide bomber struck on the road and blew himself near a Shiite shrine in Kabul, on March 20. Women and children were among the casualties, he said.
ISIL has attacked the same shrine once before, in October 2016, when gunmen killed 18 people gathered to mark Ashura, an important date for many Muslims, especially Shiites.
Afghanistan has been besieged by a wave extremist attacks since January by powerful IS affiliate groups that still remain powerful in the country.
I reiterate that under no circumstances are such attacks justifiable, and I once again call on all parties to uphold their obligations under global humanitarian law, at all times.