The Taliban denied involvement, and insist they have not carried out attacks in Kabul since February a year ago, when they signed a deal with Washington that paved the way for peace talks and withdrawal of the remaining U.S. troops.
An injured person is being brought in on a stretcher to a hospital following the blast in Kabul. Arian said that at least 52 injured people had been transported to local hospitals.
The explosion took place as students were leaving the building on Saturday, with pictures on social media showing abandoned school bags in the street.
In Dasht-e-Barchi, angry crowds attacked the ambulances and even beat health workers as they tried to evacuate the wounded, health ministry spokesman Ghulam Dastigar Nazari said.
"The entire night we carried bodies of young girls and boys to a graveyard and prayed for everyone wounded in the attack", said Mohammed Reza Ali, who has been helping families of the victims at a private hospital. He implored residents to co-operate and allow ambulances free access to the site.
"People have been evacuated to hospitals from the site", he added.
Hazaras are Shiite Muslims and considered heretics by extremist Sunnis.
Nearly exactly a year ago, a maternity unit at the local hospital was attacked, leaving 24 women, children and babies dead.
Officials said that at least 50 people were also wounded, and it is feared the casualty toll could rise. The attack occurred just as the fasting day came to an end.
The government blamed the Taliban for the carnage, but the insurgents denied responsibility and issued a statement saying the nation needed to "safeguard and look after educational centres and institutions".
Meanwhile, Pakistan strongly condemns the reprehensible attacks at a school in Kabul, Afghanistan which led to loss of many precious lives and injuries.
There was no immediate claim of responsibility for the attack, which struck a Shia Muslim neighbourhood that has been repeatedly targeted by the Islamic State group.
The Taliban and the Afghan government have traded accusations over a series of targeted killings of civil society workers, journalists and Afghan professionals.
"We call for an immediate end to this violence before any more innocent children lose their lives". While IS has taken responsibility for some of those killings, many have gone unclaimed.
No group has so far claimed the attack, but Afghan officials including President Ashraf Ghani blamed the Taliban. He offered no proof.
ISIS has previously claimed attacks against minority Shia in the same area, a year ago taking responsibility for two brutal attacks on education facilities that killed 50 people, majority students.
Saturday's attack comes days after the remaining 2,500 to 3,500 American troops officially began leaving the country.
The United States was supposed to have pulled all forces out by May 1 under a deal struck with the Taliban previous year, but Washington pushed back the date to September 11 - a move that angered the insurgents.
But the group has clashed in near daily battles in the rugged countryside with Afghan forces even as the US military continues its withdrawal.