It is understood the pensioner’s oxygen equipment caught fire in a private room of the Royal Victoria Building and there is no suggestion of any technical fault.
The fire saw 14 other elderly patients evacuated.
Police confirmed that the woman died at the scene and it is understood she had been suffering from smoke inhalation.
A spokesman said: “Police in Edinburgh can confirm investigations are at an early stage following the death of a 75-year-old woman in the Western General Hospital this morning
”Officers attended after reports were received of a small fire within a room on one of the wards. No one else was injured in the incident.”
A spokesman from the fire service also confirmed that 14 elderly patients had been evacuated from the building.
Police Scotland and the Fire Investigation Unit are now looking into the cause of the blaze.
A spokesman from the fire service said: “There is no indication to the cause of the fire right now but the fire investigation unit officers and police Scotland were at the scene this morning.
“Firefighters wearing breathing apparatus entered the ward and dealt with female patient suffering from smoke inhalation.
“They also assisted in the evacuation of the building, evacuating 15 patients in total.
The alarm was raised by an automatic fire alarm and passed to the control room at 2.30am by the switch board.
Crews from Crewe Toll, McDonald Road and Tollcross attended the blaze.
Melanie Johnson, Director of Unscheduled Care, NHS Lothian said: “We can confirm a fire occurred in part of one ward at the Royal Victoria Building during the course of the night.
“Sadly a female patient has died and our thoughts are with her family at this time.
“We are assisting emergencies services with their investigations.
“Staff responded quickly and followed well rehearsed protocols.
“A small number of patients were transferred temporarily to an adjoining ward before returning after around an hour.”