Five others were injured in the assault on the facility in Shah Wali Kot district, defence ministry spokesman Dawlat Wazir told the BBC.
It comes four days after 10 Afghan soldiers were killed when Taliban militants stormed another base in the same area.
The Taliban said it had carried out the attack, AFP news agency reports.
Last month, the Taliban announced the start of their "spring offensive" a week after killing at least 135 Afghan soldiers in a military compound near the northern city of Mazar-e Sharif.
