The property was unoccupied at the time and there were no casualties.
The alarm was raised after flames were spotted coming from the isolated house on the shores of Loch Nevis early on Saturday morning.
A spokesman for Northern Constabulary confirmed that the home was owned by Sir Cameron, who is a regular visitor to the area.
The property was unoccupied at the time and there were no casualties.
Police and fire brigade investigations into the cause of the fire have been launched.
A spokeswoman for Highlands and Islands Fire Brigade said the single storey building, named Torrach Albanach was totally destroyed in the blaze.
Firefighters attended the scene by boat as there are no roads leading to the cottage.
Sir Cameron has been credited with some of the biggest musical successes of the last 30 years, including Les Miserables, Cats, Phantom of the Opera and Miss Saigon.
He decided on his career path at the age of eight after being inspired by the show Salad Days and is one of the richest men in Britain.
In 1998, a gala concert celebrating his remarkable career and featuring scenes from his hit shows was attended by the Queen and the Duke of Edinburgh.
The estate was the target of vandalism earlier in the year when fencing was cut on three occasions.
Sir Cameron also became the target for a poster smear campaign, thought to have been connected with his plans for a tree planting scheme.
Northern Constabulary said the cause of the blaze had yet to be established and refused to speculate on a possible link with previous incidents.