The local tourism authority said it was not immediately clear whether parts of the building could be salvaged.
Police later said it burned down almost completely.
A fire alarm at the building in the Berchtesgaden district in Germany's southeastern corner went off at on Friday night, police said in a statement.
Firefighters who went to the scene could see the flames as they approached the site, on a cliff about 1800 metres above sea level.
Getting fire engines to the site proved difficult because of its location, and work was still ongoing to put out the fire on Saturday morning, police said.
The building and its immediate surroundings could only be accessed with respiratory protection equipment.
Firefighters found no one in the building and authorities believe at present that no one was injured.
A person who came into investigators' focus shortly after the fire broke out was detained, police said, but it has yet to be determined whether they had anything to do with the fire.
The building, the Kehlsteinhaus, was completed in 1938 and is reachable by an elevator inside the rock from the end of a road that winds up the mountain, in part through a series of tunnels.
The road is closed to public traffic but used by buses for visitors.
It has been operated as a cafe and restaurant since 1952 and contains an exhibition on its history.
It was not open on Friday before the fire broke out.
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