The body was found by divers contracted by Black Elk Energy, which owns the platform off the coast of Louisiana, on Saturday evening while they were inspecting the structure, said Coast Guard spokesman Carlos Vega.
Vega said he could not confirm whether the body was one of two workers who went missing after the platform fire on Friday.
He referred additional questions to Black Elk officials, who have not returned calls seeking comment.
The Coast Guard suspended its search for the missing workers early Saturday evening after three helicopter crews, a Coast Guard cutter and a plane spent the day scanning a 3625 square km area around the platform.
The blaze was touched off on Friday when workers were welding a pipe on a deck of the platform in shallow waters. Twenty-two people were on board the rig when the fire broke out and unleashed a black plume of smoke. Eleven workers were evacuated and nine others were taken by helicopter to hospitals.
The platform sits in 17m of water 27km south of Grand Isle, Louisiana, and production had been shut down since mid-August, Black Elk said.
The Bureau of Safety and Environmental Enforcement, which enforces offshore drilling regulations, is investigating.
The incident occurred a day after oil giant BP agreed to pay a record $4.5 billion in penalties for the 2010 Gulf oil spill that killed 11 workers and spewed 4.9 million barrels of oil.