Marshal Fahim National Defense University came under attack early Monday morning, the BBC reported. Security forces have swarmed into the area and blocked roads leading to it.
The attack was launched at about 5am in Monday after five insurgents attacked the academy and one is still clashing with security forces, a spokesman for the Ministr of Defence (MoD) Dawlat Waziri said. One ANA soldier is killed while 10 are wounded.
"One bomber detonated himself and another bomber was detained by our forces".
Interior minister Wais Ahmad Barmak said it is believed a second ambulance was also involved in the operation but had left the area, suggesting some would-be attackers may have escaped.
Eleven Afghan army personnel were killed and a further 16 were wounded in the attack, he added.
An Afghan security source said the gunmen had not managed to enter the heavily fortified compound, which is on the western outskirts of the city.
Witnesses told AFP they heard several explosions and gunfire at around 5:00 am (0030 GMT). Afghan officials said RPGs (Rocket-Propelled Grenade) being used and gunfire still being heard.
Militants including the Taliban and IS have stepped up their attacks on beleaguered Afghan troops and police in recent months, sapping morale already hit by desertions and corruption.
Masoom Stanekzai, the head of Afghanistan's intelligence service, said five suspects have been arrested for their involvement in the attack on the Intercontinental Hotel and that another had fled the country.