The shooter turned his weapon on the NATO troops and then was killed in the shootout, NATO said, but did not provide additional details.
NATO and Afghan authorities have launched an investigation, the international military coalition said.
NATO declined to identify the nationalities of the victims. The majority of forces in eastern Afghanistan are American.
The incident occurred in Pachir Wagam district of eastern Nangarhar province, according to an Afghan official who spoke on condition of anonymity because the information was not officially released.
It was not immediately clear if the gunman was a police officer or someone who had infiltrated the training mission. In the past, insurgents have donned police or army uniforms to attack Afghan government installations.
There have also been a number of incidents this year in which Afghan police officers turned on their trainers in deadly shootouts.
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