The Islamic State or Daesh has claimed responsibility for the latest in a series of such attacks against the Shiite community.
"At around 4 pm this afternoon, a suicide attacker who had strapped explosives to his body detonated himself inside the Mawoud education centre", police spokesman Hashmat Stanikzai said.
Afghan president Ashraf Ghani is visiting the embattled city of Ghazni, a week after the Taliban in a surprise attack managed to infiltrate deep into the key provincial capital and capture several areas.
Waheed Majrooh, a spokesman for the Ministry of Public Health said that the attack in the Shia neighbourhood of Dasht-e-Barchi left dozens more injured.
He says the victims are being taken to various hospitals in Kabul and that he fears the death toll would rise further.
In Ghazni, provincial police chief Farid Mashal said Thursday that roads were being cleared of mines planted by Taliban who temporarily held entire neighborhoods of the city that they had besieged. Scores of Taliban were also killed, according to Afghan officials.
But officials have also said they are bracing for more violence with the approach of parliamentary elections in October.
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It said 57 people were wounded in the bombing, part of spate of attacks against a branch of Islam that ISIL considers heretical. No one claimed responsibility for firing the rockets.
Elsewhere in Afghanistan, four policemen were killed and four were seriously wounded late Wednesday when they tried to defuse a vehicle bomb they found in southern Kandahar province, according to Zia Durrani, provincial police spokesman.
Before the attack on the Malikyar school, Islamic State, also known as Daesh, issued warnings through radio broadcasts and letters to schools that they would carry out attacks in retaliation for pressure their fighters were facing.
"What's crystal clear is that almost four years after the Afghan security forces took over the war efforts, they're still woefully unprepared for the task-despite very real improvements in capacities in recent years". "What we've seen over the last few days is a microcosm of the war in Afghanistan-overmatched Afghan troops, emboldened Taliban fighters, and American forces that eventually come in to help bail the Afghans out", analyst Michael Kugelman of the Wilson Center in Washington told AFP. Dilawar Aymaq, a parliamentarian from Baghlan, confirmed the attack.
The Taliban have not claimed a major assault in Kabul for weeks.
The resurgent Taliban carry out near-daily attacks against Afghan security forces, who have struggled to combat the insurgency since the US and North Atlantic Treaty Organisation formally concluded their combat mission at the end of 2014.
Also Turkey, Bahrain, the UAE, the United Nations and others condemned the attack.