Khan al-Ahmar consists of tin and wood shacks built on a desert hillside beside an Israeli highway that runs from Jerusalem to the Dead Sea.
Israel plans to demolish the village and relocate its 180 residents to a site 12 kilometres (7 miles) away. The move has drawn criticism from Palestinians and some European states, who cite the impact on the community and prospects for peace.
A spokeswoman for Israel's military liaison agency with the Palestinians said no date had been set for demolition should the houses remain after the deadline.
“This notification has been sent in accordance with the state’s obligations to enable the residents of Khan al-Ahmar to carry out the demolition independently,” she said.
Israeli security forces on Sunday morning handed out letters telling residents to voluntarily take down the buildings by October 1 or Israeli authorities would enforce the demolition orders.
“As long as your refrain from doing so, the authorities in the area will implement the demolition orders in accordance with the court ruling and the law,” the statement read.
Israel claims the village outside Kfar Adumim was illegally built.
"We will not voluntarily evacuate the place," said village resident Faisal Abu Dahuk. "The occupation forces that have an army and weapons can evacuate us by force, but there is no other place to go and we refuse to be moved anywhere else."
Palestinians say the demolition is part of an Israeli push to create an arc of settlements that would effectively cut off eastern Jerusalem from the West Bank, territories Israel captured in the 1967 Six-Day War and which the Palestinians claim for a future state.
The HCJ rejected an appeal against the demolition of the village, ruling that its stay would expire in a week and the spartan encampment could then legally be torn down