There was no sign of leaking oil from the platform located between the South American mainland and Tierra del Fuego, said Anibal Marelli, prefect of Rio Gallegos city.
An automatic warning system was activated and two rescue ships were on their way.
The fire broke out near the sleeping quarters and the galley and was not immediately brought under control.
The platform is operated by ENAP Sipetrol, a subsidiary of Chilean natural gas firm ENAP.
A fire and an explosion on an oil rig in the Gulf of Mexico off the US state of Louisiana in April killed 11 people and unleashed a massive ecological disaster as oil spilled into the water for months.