Petty officer Ryan Tippets told AFP he could no longer confirm an earlier report that two people were killed in the blaze, which was extinguished.
The incident comes a day after BP reached a deal with the U.S. government to settle criminal charges over the devastating 2010 oil spill that began with an explosion on an offshore rig.
There was no immediate news on whether any oil was spilled Friday morning from the burning platform, which is in relatively shallow water about 20 miles southeast of the beach town of Grand Isle.
"We haven't received any reports" of an oil spill, Tippets said, adding that "right now our mission is to ensure the safety of the personnel on board the platform."
The rig was not pumping oil at the time of the explosion, a spokeswoman for Louisiana's emergency management office told AFP.
"It was a fire on what is called a shut-in rig, which is one that is not actively producing oil. They were doing some work on it," said Christina Stephens of the Governor's Office of Homeland Security and Emergency Preparedness.
Local television stations showed dramatic images of thick black smoke billowing up from the platform.
There were 26 people on board when the explosion rocked the rig operated by Houston-based Black Elk Energy shortly before 9 a.m., Tippets said.
He did not have any information on the status of the nine workers airlifted to the hospital.
Black Elk Energy was not immediately available to comment.
BP agreed Thursday to pay a record $4.5 billion in U.S. fines for the 2010 Gulf of Mexico oil spill and pleaded guilty to 14 counts including felony manslaughter in the deaths of 11 workers.
The deadly blast aboard the BP-leased Deepwater Horizon rig unleashed the biggest marine oil spill in the industry's history and the worst environmental disaster to strike the United States.
It took 87 days to cap BP's runaway Macondo well, 5,000 feet below the water surface as it spewed some 4.9 million barrels of oil into the Gulf of Mexico and blackened beaches in five states.
The disaster led to major regulatory reforms, but critics say the offshore oil industry has not worked hard enough to improve its safety record.
