Ghazni governor's office said 12 of the wounded are female students of Ghazni University which is located on the outskirts of the provincial capital.
The explosion comes as Afghan security forces have been suffering scores of casualties in heavy fighting with Taliban militants in two provinces. In Ghazni province, at least 25 Afghan elite commandos were reported dead.
Afghan forces deployed to beat back Taliban fighters in Ghazni province, heavily populated by minority Hazaras, raising fears of sectarian violence. The escalation comes as Afghan government and Taliban meet for first direct peace talks in Moscow.
Afghan reinforcements were subsequently dispatched to the site of the attack in Khogyani district but were repeatedly ambushed along the way.
Officials say the fighters set fire to a government building in central Wardak district and killed the district police chief along with nine other policemen on Saturday night.
Afghan officials said US special forces units were on the ground helping to coordinate air strikes and ground operations as reports emerged that more than 300 killed on both sides, including over 100 government forces and 20 civilians.
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