Officials in the town of Alice Springs in the Northern Territory say they believe the fire was started deliberately.
The trees had been due to be added to a national heritage register.
Indigenous leaders say that the burning of the trees is a desecration – they are regarded as living spirits in indigenous culture.
Tribal elder Baydon Williams said the loss of such a revered site was “heartbreaking”.
“Those two trees symbolized a lot of sacred areas and songlines and marking of boundaries of different skin groups and different clans,” Baydon Williams said.
Songlines are pathways that cross Australia’s interior recording details of the landscape and stories told by indigenous people about creation.
“To see the trees and the way it was burned, I could feel the land, the soil around it, the area is angry and it is sad,” Baydon Williams added.
Officials say that work had recently been carried out to protect the trees from fire and to allow moisture to get to their roots.
The Northern Territory’s Minister for Indigenous Advancement Alison Anderson called the discovery “really, really sad”.
“It’s the two trees that brought this man to prominence and brought the Northern Territory and Central Australia to prominence and put us on the world map,” Alison Anderson said.
The trees feature in many of Albert Namatjira’s paintings, such as Twin Ghosts.
Art writer Susan McCulloch told the Sydney Morning Herald that the destruction of the trees was “appalling and a tragic act of cultural vandalism”.
Albert Namatjira was born in 1902 at the Hermannsburg Mission in the Northern Territory and was a traditional custodian of the lands of the Arrernte people in that area.
Growing up, Albert Namatjira made sketches of scenes around him and later made images for mulga wood plaques.
In 1934, Albert Namatjira saw an exhibition at Hermannsburg organized for an indigenous audience showing landscape works by Australian artists like Rex Battarbee and John Gardner.
He then took up painting himself, having his first solo exhibition in Melbourne in 1938.
Albert Namatjira earned widespread acclaim for his vivid landscape paintings of the central Australian desert.
He is credited with helping to change the perception of Australia’s interior from that of the country’s “dead heart” to one of a vital space, imbued with spiritual significance for indigenous peoples.
In 1957 he was granted full Australian citizenship, as opposed to other indigenous people, who were considered wards of state in the Northern Territory.
In 1958 Albert Namatjira spent two months in prison for a charge of supplying alcohol to other indigenous people. Citizens were entitled to procure alcohol, but it was illegal to supply to wards of state, including indigenous people. Albert Namatjira died in 1959.
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