The New York Times, quoting Ezmarai Nasiri, the Afghan police chief in the area, reported the plane's tail caught fire after it crashed Monday. Bagram Air Base is near Kabul.
The cause of the crash was under investigation. Military officials said there was no enemy activity in the area at the time the plane went down, the Times said.
It was not immediately known where the plane was headed or whether it was carrying any cargo.
The Times said the plane was operated by National Air Cargo, a military contractor from Orchard Park, N.Y.
The Taliban reportedly said they had shot down the plane, but the Wall Street Journal reported coalition forces dismissed the claim. The report said the crash site is within the perimeter of the air base.
The plane crash was the second since Saturday.
In the Saturday incident, a military turboprop plane crashed in southern Afghanistan, killing four U.S. airmen, the Los Angeles Times reported. The report said the U.S. Defense Department had identified all four victims.