Logar province is just south of Afghanistan’s capital, Kabul.
The six US crew members injured in the crash are receiving medical treatment.
The statement said the crash was not a result of enemy action and its circumstances are being investigated.
“We have full accountability of all personnel and the crash site has been secured,” the statement adds.
“We are deeply saddened by the loss of our comrade,” said Army Gen. John Nicholson, Resolute Support commander.
“On behalf of all of Resolute Support, our heartfelt sympathies go out to the families and friends of our fallen comrade and those injured in this unfortunate event.”