NATO officials confirmed the shooting at the British-run Afghan National Army Officer Academy, which has been set up to produce a new generation of professional military leaders as the Afghan army takes on the Taliban.
"There was an argument between two soldiers that led to violence and each of them opened fire," Dawlat Waziri, a spokesman for the Afghan defence ministry, told AFP.
The Afghan soldier was killed and two international soldiers received minor injuries in the shooting yesterday.
The academy welcomed its first batch of recruits on October 19 and is due to be formally opened at a ceremony on tomorrow.
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Officials, speaking on condition of anonymity, said that none of the cadets were involved in the shooting.
"One of our instructors at the Afghan army officer academy was doing a task in the adjacent Afghan unit," New Zealand Lieutenant General Rhys Jones said, according to the Australian Broadcasting Corporation.
"He was escorted by two Australian force protection people, as they were coming back from that meeting, without notice an Afghani soldier, a single Afghani soldier, shot at them."
At a media opening day on Wednesday, the first intake of cadets was put through their paces on the parade ground, as trainers said the 42-week course would transform men into officers who would one day lead the Afghan army.
The Afghan military has been built from scratch since the fall of the Taliban regime in 2001, and it has struggled with high casualty rates, "insider attack" killings, mass desertions and equipment shortages.
Attacks in which Afghan forces turn their guns on their international partners have killed scores of NATO-led troops, breeding mistrust and undermining efforts to train local forces before NATO combat troops withdraw next year.