Benjamin Netanyahu, the Israeli prime minister, announced the plan four days after a barrier to keep out illegal African migrants was erected along the border with Egypt.
"We know that on the other side of our border with Syria today, the Syrian army has backed off, and global jihad operatives have taken its place," Mr Netanyahu told a cabinet meeting. "We must therefore protect this border from infiltrations and terror."
Mr Netanyahu reiterated Israeli fears over Syria's chemical weapons falling into the hands of Islamist groups.
"We are coordinating our intelligence and readiness with the US and others so that we might be prepared for any scenario," he said.
Building a barrier in the Golan Heights would consolidate Israel's hold on territory that it seized from Syria in the 1967 Six-Day War and annexed in 1981 in a move that has never been internationally recognised.
Negotiations over a deal that would lead to an Israeli withdrawal have led nowhere. In 2009, Mr Netanyahu said that returning the territory would turn it into "Iran's front lines which will threaten the whole state of Israel".