The attack took place in eastern Afghanistan on Monday, a statement from the NATO-led Resolute Support mission said.
It was not immediately clear who carried out the attack.
However, the statement said it was “an apparent insider attack”.
The wounded service member is in a stable condition, the statement added.
The name of the fallen soldier will be released 24 hours after next of kin notification, NATO concluded.
According to the statement, the U.S. service member is the sixth American killed in Afghanistan this year.