"The ceasefire went on effect this morning", interior ministry spokesman Najib Danish said.
The attack happened as employees at the Department of Rural Rehabilitation and Development left early for Ramadan.
Referring to border fencing, the Army Chief said that this is an obstacle for checking terrorism and not between people of both sides.
Noori said that elsewhere in Ghazni, at least three local police and 10 Taliban were killed in clashes.
No group has yet claimed responsibility for the bombing.
A suicide bomber blew himself up at the entrance to the education department, triggering a fierce battle between gunmen and Afghan security forces, Nangarhar provincial governor spokesman Attaullah Khogyani told AFP.
Police operation in Paris as man holds 2 hostages
Emergency services arrive at the scene of a hostage situation in central France on Tuesday, June 12, 2018. Police say a man is holding two people hostage in an office in central Paris .
The three wounded were detained after police found explosives, including suicide vests, in the building they suspect was being used by militants planning attacks in the city.
Ghani on Thursday announced police and troops would halt hostilities with the Taliban for eight days - though he warned that operations against other groups, including Islamic State group, would continue.
The Humvee was taken earlier by Taliban forces from the Afghan forces in a separate attack, said Noori.
Relatives mourn a victim after a deadly suicide attack in Kabul on June 11.
COAS congratulated Afghanistan authorities on recent peace initiatives especially in respect of the holy month of Ramadan/ Eid and wished that these steps gain more of permanence ultimately leading towards an enduring peace. However, they will retaliate with full force in the event of coming under attack.
The Taliban's announcement has meanwhile brought renewed hope for the resumption of the stalled peace process between the Afghan government and the militants. They said they would continue attacking US-led North Atlantic Treaty Organisation troops.
The latest violence comes as dozens of protesters march hundreds of kilometres towards Kabul to demand an end to the almost 17-year conflict.