The fatal blast killed 29 and wounded another 52 people, Ministry of Public Health spokesman Wahid Majroh revealed.
The Persian new year, known in Afghanistan as Nauruz, is a national holiday.
The explosion occurred in a civilian-populated area of Kabul, where Afghans had gathered peacefully to celebrate Nowruz, the beginning of the new year. The Islamic State (ISIS, for its acronym in English) has assumed authorship of massacre, according to Amaq, news portal akin to jihadist group, quoted by France Presse (AFP).
News reports quoted the interior ministry as saying that a suicide bomber had detonated his explosives while walking among a group of people. Women and children were among the casualties, he said.
Afghanistan's Shiite population has repeatedly been targeted by IS affiliates, who view the minority group as apostates of Islam.
Boy wounded in Maryland high school shooting out of hospital
Agents from the federal Bureau of Alcohol, Tobacco, Firearms and Explosives have also been sent to the school. Mary's County, with a population of about 110,000, is about 65 miles (105 kilometers) from Washington, D.C.
Kabul's police chief, General Daud Amin, said the bomber had managed to slip past police checkpoints set up along the road.
"We had our security in place in and around the shrine", he said. Officials reveal that 26 people were killed and 18 others were injured in the terror attack.
Some Western and Afghan security experts believe the Haqqani Network, a hard-line wing of the Taliban, has been behind some of the attacks in Kabul in recent months, including those claimed by ISIL.
The March 21 festival is celebrated mainly in Iran, Afghanistan, India, and Turkic republics such as Azerbaijan, Caucasus countries, Albania and Macedonia.
I reiterate that under no circumstances are such attacks justifiable, and I once again call on all parties to uphold their obligations under worldwide humanitarian law, at all times.