It was initially reported that oil was leaking from the Mariner Energy-owned platform. But hours later crews determined there was no spill.
The rig was located 90 miles south of Vermillion Bay, Louisiana.
The platform is connected to seven active wells, but they were shut down for maintenance at the time.
The 13 workers who were on the platform were rescued after jumping into the water.
Thursday's fire came less than five months after the explosion of the Deepwater Horizon oil rig that killed 11 people and spurred the worst offshore oil spill in the nation's history.
It's still unclear what caused the fire.
The Associated Press contributed to this story.