The attack, which comes as cadets were returning to the academy after their two-day weekend, marks a serious breach of security at a premier training institute for Afghan security forces.
"A suicide bomber on foot blew himself up near the academy," said Deputy Interior Ministry Spokesman Najib Danish. "Heavy casualties are expected."
Kabul Deputy Police Chief Gul Agha Rouhani confirmed the suicide attack but refused to comment on possible casualties.
The bombing comes less than 24 hours after a truck bomb tore through central Kabul, killing 15 civilians and wounding 240 others in the first major attack in the Afghan capital since the announcement of Taliban leader Mullah Omar's death.
No group immediately claimed responsibility for either of the attacks, which come as the Taliban steps up their summer offensive despite a bitter power transition within the militant movement.
The carnage comes a day after Taliban insurgents killed nine people in multiple attacks on police targets, including a truck bombing in the volatile eastern province of Logar.
The uptick in attacks highlight growing insecurity in the country amid a faltering peace process with the Taliban as Afghan forces face their first summer fighting season without full NATO support.
A UN report published Wednesday said civilian casualties in Afghanistan hit a record high in the first half of 2015.
The report said 1,592 civilians were killed, a six percent fall from last year, but the number of injured jumped four percent to 3,329.
Overall, casualties reached their highest level since the UN began issuing its authoritative reports in 2009.