The three wounded were Slovakian troops, said Kandahar airfield commander Gen. Abdul Raziq Sherzai. Slovakia guards the important base in southern Afghanistan.
The shooter was taken into custody after the morning incident and was questioned, said Kandahar government spokesman, Javid Faisal.
Faisal said a preliminary investigation indicates the shooting was an "accident" rather than a so-called insider attack.
Officials had initially said the Afghan soldier fired on Americans and that there had been no casualties.
The NATO-led coalition would only confirm an attack in southern Afghanistan, and referred all other questions to Afghan authorities leading the investigation.