No group immediately claimed responsibility for the dawn attack, which comes after nearly three months of relative calm in Kabul.
Twelve others were wounded, spokesman Nasrat Rahimi said in a statement.
“It was a big explosion that rocked our house. We also heard gunfire afterwards. Ambulances rushed to the area quickly,” resident Samiullah, who like many Afghans goes by one name, told.
A security source speaking on the condition of anonymity told that the attacker was on foot when he targeted a vehicle near a checkpoint as it was entering the academy.
President Ashraf Ghani slammed the attack, calling the bombing “a crime against humanity” while repeating his call for a nationwide ceasefire.
Taliban spokesman Zabihullah Mujahid said he was unaware of any claim for the bombing, adding that the insurgents were “investigating” the incident. The Islamic State group are also active in Kabul.
In recent weeks the Taliban have refrained from attacking major urban centres in an effort to keep talks with the US on track, but violence in the provinces has continued.
The last major attack in Kabul was in November, when at least 12 people were killed after a minivan packed with explosives rammed into a vehicle carrying foreigners during morning rush hour.
Four foreign nationals were among those wounded in the attack.
There appears to have been little progress in reaching a deal in recent weeks, however, prompting the insurgents to saddle blame on the White House and what they say are a growing list of demands.
The US and Taliban had been negotiating for a year and were on the brink of an announcement in September 2019 when President Donald Trump abruptly declared the process “dead”, citing ongoing violence.
As talks have fluctuated, violent attacks in the country have raged, with the number of clashes jumping to record levels in the last quarter of 2019, according to a recent US government watchdog report.