State-run oil company Petroleos Mexicanos, or Pemex, said it had averted any significant oil spill following the blast, which also injured 16 workers, two seriously, and forced the evacuation of 300.
Pemex later said a total of 45 workers had received some form of treatment or health evaluation.
Firefighters were still working to put out the fire, which was consuming the oil that was on the platform, Pemex Director General Emilio Lozoya said late Wednesday afternoon, adding that efforts were "on the right track." Ten firefighting and emergency boats were being used.
Speaking at a news conference in the nearby city of Ciudad del Carmen, Lozoya said the cause of the fire was still being investigated, but it appeared to be something mechanical.
Helicopters ferried workers with bandaged hands and faces and burn marks on their overalls to Ciudad del Carmen, where crowds of relatives of oil workers thronged outside hospitals.
A survivor of the blaze on the shallow-water Abkatun-A Permanente platform in the Campeche Sound said workers "jumped into the sea out of desperation and panic."
"There was nothing you could do but run," said Roger Arias Sanchez, an employee of Pemex contractor Cotemar who escaped the burning platform in an evacuation boat.
Many of the injured appeared to be Cotemar employees.
In a statement later Wednesday, Pemex said the accident "did not cause an oil spill into the sea, given that there was only a seepage, which is being taken care of by specialized vessels."
The company said it had been able to cut off pipelines to avoid a spill, and suggested that the oil remaining in the pipelines was burning off.
Lozoya said the accident "would have a minimal impact on production, because this was a processing platform," not a producing well. Production from nearby wells it normally serves could be rerouted to other processing platforms.
President Enrique Pena Nieto promised an investigation to "find whoever is responsible" and avoid such accidents in the future.
The Abkatun A platform largely serves to separate gas, oil and other petroleum products, and pump them to refineries onshore.
Previous spills from Mexican facilities have usually occurred at active offshore wells, not processing stations.
The Abkatun platform lies off the coast of the states of Campeche and Tabasco. It is farther out to sea than the platform involved in the last severe fire in the area, a 2007 blaze at the Kab 121 offshore rig.
That accident was caused by high waves that hit the rig, sending a boom crashing into a valve assembly. The blaze killed at least 21 workers and the rig spilled crude and natural gas for almost two months.
Mexico's worst major spill in the Gulf was in June 1979, when an offshore drilling rig in Mexican waters, the Ixtoc I, blew up, releasing 140 million gallons of oil. It took Pemex and a series of U.S. contractors nearly nine months to cap the well, and a great deal of the oil contaminated Mexican and U.S. waters.
Pemex has had serious security problems in the past, mainly in its onshore pipeline network, where thieves drilled around 2,500 illegal taps in the first nine months of 2104 and stole more than $1 billion in fuel.
That problem got so bad that in February, the company announced it would no longer ship finished, usable gasoline or diesel through pipelines.
That apparently hasn't stopped the thieves, though. On Wednesday, federal police announced they had seized three tanker trucks and 148,000 litres (39,100 gallons) of stolen fuel at several different sites throughout the country as well as locating two illegal pipeline taps.