This move on Sunday came one day before the start of a UN court hearing into the project's legality.
In line with an announcement made earlier by the defence ministry, the radio said an eight-kilometre stretch of the barrier that enclosed the Palestinian town of Baqa al-Sharqiya inside an enclave in the northern West Bank was being taken down.
"We are going to dismantle the eastern fence (around Baqa al-Sharkiya) as we said we would do many months ago," said Rachel Niedak Ashkenazi on Saturday. She said the move would give residents free access to the rest of the West Bank.
Askenazi said the timing of the announcement was not unrelated to the upcoming hearings at the International Court of Justice (ICJ), due to start on Monday.
"The removal of the eastern section was due to happen at the end of 2003 but it had been delayed," she said, admitting the ICJ hearings had "something to do with it".
Until now, the seven thousand Palestinians cooped up inside the enclave could only access the West Bank through a series of security gates.
Another section of the barrier, which lies to the west of the village, makes it impossible for residents to reach Israel.
Askenazi said the dismantling operation was likely to take "weeks rather than months," while refusing to comment on the costs. Israel's private Channel 10 reporting late on Friday, gave an estimate of $8 million.