CSX did not immediately respond to an emailed request for comment. No injuries or fatalities were immediately reported.
The Mount Carbon area is just over 30 miles south-east of Charleston, West Virginia.
Evacuation orders have been issued for two nearby towns, Adena Village and Lower Boomer, with at least one house fire also reported, according to the Charleston Daily Mail.
“At least one, possibly more, rail cars have gone into the Kanawha River,” the newspaper quoted the state Department of Military Affairs and Public Safety spokesman Lawrence Messina as saying.
“We’re told that emergency responders are having a hard time reaching the house fire because of the derailment.”
Reuters reported that it was not immediately clear where the train was heading, where its cargo originated or whose oil it was carrying.
The crash occurred less than 200 miles (320 km) west of Lynchburg, Virginia, where another CSX train bound for an East Coast oil terminal run by Plains All American Pipelines derailed and erupted in flames last April, the news wire said.
The West Virginia incident is the second such crude-train derailment in three days, with Canadian investigators probing a northern Ontario site where seven rail cars were reported to be ablaze.
North American rail safety has become a major area of concern following that incident as volumes of crude oil from unconventional plays such as the Bakken have risen exponentially in recent years.
Last September US rail regulators proposed major upgrades to transportation rules following a rash of train derailments, including the deadly Lac-Megantic runaway-train accident in Quebec in July 2013, which killed 47 people.