The emergency services were called to the property in the Sangomore area of Durness at about 02:00.
Police Scotland said it was not known if she was in the house at the time. Her relatives have been informed.
Det Insp Richard Baird said the fire was not thought to be suspicious, but the damage caused had prevented entry to the property.
He said: "A joint investigation with the fire service will be carried out.
"Enquiries are at a very early stage, however, initial enquiries would suggest there are no suspicious circumstances.
"Due to the extensive structural damage and uncertainty of the building, gaining access to the property will take some considerable time.
"Structural engineers will advise when it will be safe to enter the property."

The International Paralympic Committee (IPC) suspended Russia from the Rio Games starting on 7 September because of state-sponsored doping.
Putin said the ruling was "cynical" and "humiliates those who take such decisions".
Only Russian track and field athletes were banned from the Olympics.
Putin, speaking at an award ceremony for Russian Olympians at the Kremlin, said the country would hold special competitions for banned Paralympic athletes, with the winners awarded the same prizes as in Rio.
Foreign ministry spokeswoman Maria Zakharova said Russian Paralympians had taken "collective responsibility for an unproven crime".

Police were called to a unit at Derwent Works, Matlock Road, Ambergate, at about 20:00 BST on Sunday following reports a man had been injured.
The man, believed to be 19, was later confirmed dead in hospital.
A file is being prepared for the coroner, but the force does not believe there are any suspicious circumstances surrounding the death.

The 34-year-old Canadian joins the Giants from the Austrian Hockey League side Villacher SV.
Johner was selected by the Florida Panthers in the 2001 NHL draft but has played in Europe for the past decade.
He won the Swiss A League with the Zurich Lions and had a successful spell in the Swedish League.
Johner becomes the fourth new signing of the summer for the Giants following the arrivals of Darcy Murphy, Jonathan Ferland and Sebastien Sylvestre.
"Johner is one of those guys that no matter who you speak to about him, they have nothing but positive things to say - as a player, person and team-mate," said Giants head coach Adam Keefe.
"We are really excited to add a player of Dustin's pedigree to the Belfast Giants. He's another new signing that will leave it all out on the ice for this city."
Police are trying to trace a woman who is unaccounted for after a fire at her home in the Highlands.
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Russian President Vladimir Putin says the country's Paralympics ban is "outside the bounds of law, morality and humanity".
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A man has died after apparently falling through the roof of a building at an industrial site in Derbyshire.
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The Belfast Giants have added experienced forward Dustin Johner to their roster for the forthcoming Elite League season.