The statement says US forces came under fire during an early morning search of a compound near Shindand airfield in Herat province, which borders Iran.
"One US soldier and one Afghan citizen were killed in an exchange of fire in Shindand when US soldiers were searching a compound," Major Mark McCann said.
"No further details are available at this time," McCann added.
The Afghani civilian was killed at the scene while the US soldier died a short time later at the airfield as a result of his wounds, the statement said.
The soldier's name was being withheld until his next of kin could be notified.
The military did not identify the Afghan, or say whether he was a fighter or a bystander.
But a local commander, Akhtar Muhammad Husaini, said the compound belonged to a former commander in the region, Mullah Dost.
Exchange of fire
"There was fire from both sides. Mullah Dost was killed along with his wife, and two of their children were injured," Husaini told Associated Press by telephone. "The Americans wanted to search his house, but we don't know who fired first."
"There was fire from both sides. Mullah Dost was killed along with his wife, and two of their children were injured"
Akhtar Muhammad Husaini,
Former regional commander
US and Afghan government forces have been stationed at Shindand airfield, about 650km west of the capital, Kabul.
It was unclear if Sunday's search, which the US military described as "routine," was aimed at suspected Taliban fighters or part of efforts to disarm local commanders.
Some 18,000 US-led troops are still stationed in Afghanistan, in search of what they say are remnants of al-Qaida and the Taliban.