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Crescent in The Grange around 8.20am yesterday morning.
It is understood that some of her injuries, and those of the dead man in the property, were not caused by the fire.
Police sources reportedly said the 30-year-old had been stabbed and the other man in the flat had been battered to death.
Officially, police said they were “keeping an open mind” over the cause of death. A spokesman said they still did not know the man’s identity, and appealed for anyone with information to come forward.
The injured woman, named locally as Ms Methven, was treated at the scene before being taken by ambulance to Edinburgh Royal Infirmary with smoke inhalation.
Last night police were waiting to interview Ms Methven over the incident and were reportedly poised to launch a murder investigation. It is understood Ms Methven is not being treated as a suspect.
Police and the fire service are conducting a joint investigation to establish the cause of the blaze and could not rule out the possibility it had been started deliberately.
Part of Chalmers Crescent between Palmerston Road and Grange Road were cordoned off all day, with police allowing access only to residents.
One neighbour, who lives in the block of flats where the drama unfolded, said fire damage at the ground floor flat appeared to be minimal.
“I was able to see into the hallway of the flat and it doesn’t seem to be a serious fire at all. There was a little bit of smoke damage but it didn’t seem like a particularly dangerous fire. There was no [debris] in the stair or anything.
“I was at work but came home after a neighbour called to say there had been a fire in my block. Obviously I’ve heard someone was found dead in there, which is surprising especially in a neighbourhood like this.
“There have been plain clothes police, CID and forensics teams all in their white protective suits here all day.”
He added: “As far as I was aware she was only a single girl living there on her own. If there was anyone living with her I never noticed them and I’m in the same block”
Detective Inspector George Thomson, who was on the scene, said: “We are investigating the death of a man who died in a suspicious fire that broke out in a property in Chalmers Crescent at around 8.20am [on Monday].
“A woman who was rescued from the ground-floor property is being treated in hospital.
“We are working with the fire service to establish the cause of the blaze.
“We are appealing for anyone who was in the area of Chalmers Crescent at the time the fire broke out, who noticed any suspicious activity, to contact police on 0131-311 3131, or Crimestoppers on 0800-555 111.”