The Taliban have claimed responsibility for the shooting at the Afghan air force facility attached to the airport, although the insurgents sometimes make false or exaggerated claims.
The defence ministry reported several people killed and injured and said the clash arose from an argument.
"At around 11:00am (0630 GMT) within the air force compound, an argument took place between an [Afghan] air force officer and foreign colleagues," the ministry said in a statement. "An exchange of fire followed. A number have been killed and injured. Details will come later."
Nato efforts to train and equip local forces into taking over responsibility for security by 2014 have been hit by a number of attacks carried out by rebels who have apparently infiltrated the armed forces or committed attacks wearing unauthorised uniforms.
The defence ministry in Kabul was targeted last week by a gunman in army uniform wearing a suicide vest, in an attack that left three people dead.
The international police agency, Interpol, on Wednesday dubbed Sunday’s mass jailbreak by Taliban fighters “unacceptable”.
"It is simply shocking that three years after the largest jail break in Afghanistan history, including of convicted terrorists, there is no data to be shared with law enforcement, regionally and globally," Interpol secretary general Ronald Noble said. "Until this glaring and serious void in the world's anti-terror efforts is filled, no country can consider itself secure from criminals and terrorists who are essentially being given an opportunity to travel internationally."
Noble made it clear that criticism of the event applied not only to Afghan authorities but also to international forces which are supposed to be training them and reconstructing Afghanistan.