The Ministry of Education (MoE) said the incident took place this morning in Bak district after a mortar round landed in a primary school.
A statement by MoE said two female students were among those killed in the attack, urging the Afghan security institutions to take immediate steps in identifying and trying those involved behind the incident.
No group including the Taliban militants has so far claimed responsibility behind the attack.
Khost is among the relatively volatile provinces in southeastern Afghanistan where anti-government armed militant groups including the notorious Haqqani network insurgents are actively operating in a number of its districts.
Found in the late 1970s by Jalaluddin Haqqani, the terrorist network is accused of staging numerous cross-border attacks from their base in North Waziristan, including the 19-hour siege at the US Embassy in Kabul in September 2011.
The network is allied with al-Qaida and the Afghan Taliban and cooperates with other terrorist organizations in the region and was designated a Foreign Terrorist Organization on September 7, 2012 by the US Department of State.