On Tuesday, Pemex said the refinery in the northern state of Nuevo León had been shut down due to low water pressure from a nearby river that supplies the facility's boilers.
Rowdy teacher protests in southern Mexico have caused delays and bottlenecks in transporting fuel from the country's top refinery in Salina Cruz.
The refinery suspended operations due to an interruption in its steam supply.
The company did not say how the fire started, or when it expected to finish putting it out.
The blaze apparently started in an area used to store stolen fuel.
The refinery upsets come as Mexican gasoline demand has prompted a slew of cargo bookings from West Coast hubs.
The unplanned outages coincide with an uptick in demand from Mexico following a fire at that country's largest refinery in November.
Four workers suffered burns and were taken to a local hospital, another worker fell as he operated a fire hose during the emergency response.
Pemex said in a statement that firefighters had controlled Tuesday's blaze at the Antonio Dovali Jaime refinery in the southern state of Oaxaca.
As Pemex processes less oil, the utilization rate of its six domestic refineries - the volume of crude processed divided by refinery capacity - could sink to as low as 63 percent this year.