Divers hired by the platform owner, Black Elk Energy, made the discovery Saturday night.
The company says the body appears to belong to one of two crew members who jumped into the water when the platform exploded.
Black Elk Energy CEO John Hoffman said the body was found by a contract dive vessel. He said a second dive vessel has been brought in to speed up the search for the second missing worker.
Hoffman said the missing men were employees of oilfield contractor Grand Isle Shipyard.
After Friday's blaze, 11 people were taken by helicopter to area hospitals or for treatment on shore by emergency medical workers.
Meantime, company officials say no oil is leaking from the charred platform.
Early Sunday, the Philippine Embassy in Washington said the worker whose body was recovered was Filipino, as are the worker who remains missing and four who have been hospitalized. The embassy declined to release names and expressed its condolences to the family of the dead worker.
The cause of the fire was under investigation.
The Associated Press contributed to this report.