Fifteen others have been injured. Half of them are thought to be Americans and they also include a German general.
Afghanistan’s Ministry of Defense said the Afghan soldier was shot dead after he opened fire.
The major-general is the most senior international soldier killed since the fall of the Taliban in 2001.
The attacker was a soldier who was recruited three years ago.
The incident is said to have occurred late morning or lunchtime after a dispute between Afghans and an armed Afghan soldier.
The Afghan soldier opened fire from a guard post at a large group of senior Afghan and international troops.
By the time he had emptied the magazine of his US-issue M16 rifle, more than a dozen people had been shot, our correspondent says.
The Afghan commander of the British-led officers’ academy, General Gulam Sakhi, was among those wounded, and German military sources said a German general was also hit. At least one British soldier was also wounded.
The training academy is modeled on UK military academy Sandhurst and will be the only British military presence in Afghanistan when operations end this year.
The NATO-led International Security Assistance Force (ISAF) said in a statement: “We can confirm that an incident occurred involving local Afghan and ISAF troops at Camp Qargha.
“The camp, also known as the Kabul ANA Officer Academy, is an Afghan National Security Forces facility. We are in the process of assessing the situation.”
The academy is set in a long, low ridge of hills close to Kabul.
Its military history syllabus includes the analysis of Afghan tactics in past wars against the British, as well as during the mujahedeen wars against the Soviet army.
There were 10,000 applicants who applied ahead of its first intake.
Shortly after the academy opened there was a shooting incident when an Afghan soldier in a neighboring barracks opened fire, injuring Australian and New Zealand troops providing security.
There are also troops from other nations at the site, including a large contingent of US soldiers.
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