Afghan Interior Ministry spokesman Nasrat Rahimi said 12 people were also wounded in the February 11 blast, including five civilians.
The Defense Ministry put the number of people wounded at six.
No group immediately claimed responsibility for the attack, which took place at a checkpoint near the entrance of the government-run Marshal Fahim Military Academy in a southwestern section of the city, according to Rahimi.
Ambulances arrived on the scene after the explosion, which happened around 7 a.m. local time as employees and cadets were entering the academy.
A witness said there was a big explosion followed by gunfire.
The academy has been the scene of several attacks in the past, including an assault in May last year that was claimed by the Islamic State (IS) extremist group.
The latest attack appeared to be the first major assault in Kabul in months.
It comes as U.S. and Taliban negotiators wrangle over a possible peace deal to end the nearly two-decade war.
On February 10, President Donald Trump traveled to Dover Air Force Base in Delaware to pay respects to two U.S. soldiers killed this weekend in Afghanistan.
The two U.S. servicemen were killed and six others were wounded in Afghanistan’s eastern Nangarhar Province on February 8 when a soldier dressed in an Afghan National Army uniform opened fire with a machine gun.
A total of six U.S. service members have been killed in Afghanistan since the start of the year.