The incident marks the first US combat death in Iraq since troops returned to the country in 2014 to fight the Islamic State terrorist group*, the Wall Street Journal reported citing defence officials.
Koppenhafer was killed during an operation against a suspected IS target in the Iraqi province of Nineveh, the report said.
The Department of Defense in a statement said Koppenhafer died on Saturday after sustaining injuries from "enemy small arms" fire during the operation. However, the Pentagon also said a probe into the incident was underway.
The United States and its allies have been fighting the Daesh* terror group in Syria and Iraq since 2014. While Iraqi authorities have given permission to host foreign troops in the state, a campaign in Syria by coalition forces is conducted without the approval of the government or a mandate from the UN Security Council.
* Daesh (ISIL/ISIS/IS/Islamic State) is a terrorist organisation banned in Russia