The wounded troops are being treated and are in stable condition, officials with the Resolute Support mission said in a statement.
The incident is under investigation.
The name of the service member killed in the incident will not be released until family members are notified, officials said.
Saturday’s incident marks the first U.S. troop death in Afghanistan in more than two months.
Spc. Gabriel Conde, 22, was killed April 30 as a result of enemy small arms fire in eastern Afghanistan, officials said at the time. Another soldier was wounded in the same incident.