Coast Guard Petty Officer Carlos Vega told CBS News that the fire, which has been put out, was the result of an oil rig explosion approximately 20 nautical miles southeast of Grand Isle, La.
CBS Houston affiliate KHOU-TV reports two workers had died and another two were missing, according to the Coast Guard.
Four other injured workers were air-lifted to a hospital, Kirk Trascher, a spokesman for the rig's owner, Black Elk Energy in Houston, told KHOU-TV.
A Louisiana parish official says the rig is not drilling at a deepwater site like the Macondo well that blew out in 2010. That blowout led to an explosion that killed 11 workers and led to the worst offshore oil spill in U.S. history.
Jefferson Parish Councilman Chris Roberts told CBS New Orleans affiliate WWL-TV that the platform is a shallow water platform in the Gulf of Mexico. It is near West Cote Blanche Bay, south of New Iberia on the south-central Louisiana coast.
The Coast Guard says it has activated a command center to investigate the fire.
The size of the fire was not immediately clear.