The so-called "green-on-blue" attack was the latest in a series of incidents in which Afghan forces have turned their weapons on international troops with whom they are working.
The last time a US soldier was killed in an insider attack was on July 7 in the country's south.
General Scott Miller, who took command of US and NATO forces in Afghanistan on Sunday, said the soldier's death was "a tragic loss".
US soldier killed in 'apparent insider attack' in Afghanistan: NATO
"Our duty now is to honour him, care for his family and continue our mission," Miller said in a statement.
The wounded soldier was in a stable condition, the statement said.
NATO did not release the identity of the American soldier killed or provide further details about where the incident took place.
Currently, there are about 14,000 US troops in Afghanistan, providing the main component of the NATO mission there to support and train local forces.
American casualties have fallen dramatically since the withdrawal of US-led NATO combat troops at the end of 2014.
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