Alizee Sery, 25, climbed to the top of the sacred rock and was filmed stripping down to a bikini, an act she described as a "tribute" to Aboriginal culture.
The Federal Government asks tourists not to climb Uluru and to respect the site when they visit.
But the Central Land Council's director, David Ross, says the woman's stupidity is indicative of many people who ignore the traditional owners' request not to climb the rock.
He says the climb should be closed and Prime Minister Julia Gillard to deport the woman.
Traditional owner Alison Hunt says she too is angry and disgusted by the Ms Sery's lack of respect for Indigenous people living in the area.
"We try our best to share our land with many walks of life and coming here and doing that is just disrespect - it's not acceptable at all," she said.
But Ms Sery has told the Sunday Territorian that she meant no offence.
"I am aware that Uluru is sacred in their culture. My project is a tribute to the greatness of the Rock," she said.
"What we need to remember is that traditionally, the Aboriginal people were living naked. So stripping down was a return to what it was like.
"After such a hard climb, when you reach the top, the view and the magic of the place gives you an amazing feeling of peace and freedom. You want to sing, dance and strip."
This makes me think is that we really need legislation to ban the climbing of Uluru. Other Australians agree/disagree?