Eight firefighting vessels were battling the early morning blaze at the Abkatun Permanente platform on the Gulf of Mexico's Campeche Sound, the state-run firm said.
The blaze took place in the dehydration and pump area of the platform, located off the coast of eastern Campeche state, Pemex said in a statement.
"Regrettably, we confirm the death of a worker from the Cotemar company," a Pemex contractor, the firm said, adding that two of the injured workers are in serious condition.
The fire is latest incident to hit the state oil firm in recent years.
In January 2013, a gas buildup caused an explosion at the company's Mexico City headquarters, killing 37 people.
President Enrique Pena Nieto pushed through a sweeping energy reform bill last year that opens the sector to foreign investors in a bid to reverse falling production and modernise ageing infrastructure.