The fire has been extinguished, Black Elk spokeswoman Leslie Hoffman said. She said an emergency response is under way but declined further comment, saying the company will issue a statement later Friday.
The U.S. Coast Guard said 11 people were airlifted to hospitals, while nine others were evacuated to other nearby energy facilities. Search and rescue helicopters were scouring the area, located around 17 miles south of Grand Isle, Louisiana.
No fatalities have been confirmed, but two workers are missing. The 11 hurt included four who suffered burns and were in critical condition at Louisiana's West Jefferson Medical Center, a hospital spokeswoman said.
When it caught fire, 22 workers were aboard the shallow-water platform, which was not actively drilling or producing oil and gas, the Coast Guard said.
An oil sheen is being monitored in waters nearby. The Coast Guard said there appeared to be little risk of a major oil spill, because production was shut off before the fire, and Black Elk told authorities that any spill could be as little as 28 gallons.