Barak was touring the Golan, which Israel captured from Syria in the 1967 Mideast war, a day after three top officials in the regime of President Bashar Assad were killed in a suicide attack in Damascus. Israeli defense officials are closely monitoring the deteriorating situation in their neighbor to the north, worried it could spill across the frontier.
Mortar shells fell about one kilometer (half a mile) from where Barak stood, and bullets flew as rebels and Syrian army forces skirmished, according to a statement his office released.
With fighting licking at the Israeli-held frontier, Barak observed that Syrian refugees, who have already started fleeing to Turkey and Jordan, might also start streaming toward the Golan.
"If we have to stop waves of refugees we will stop them," he said in the statement.
Past efforts to block crowds trying to storm the Golan have turned deadly. Twice in 2011, hundreds of pro-Palestinian protesters tried to enter the territory from Syria, touching off battles with Israeli security forces.
In the first instance, Israel was caught off guard, and hundreds breached the frontier, entering the Golan for several hours. Israel has since stepped up security in the area.
The deteriorating situation in Syria has become a mounting concern for Israel, which fears that the collapse of a central regime would give Lebanese Hezbollah militants an opportunity to raid Syrian military arsenals for chemical weapons or sophisticated missiles that could strike Israel. The Syrian-backed Hezbollah warred Israel to a draw in the summer of 2006.
While Syria and Israel are bitter enemies, the border has been mostly quiet since 1974. Some Israeli officials worry the departure of the four-decade Assad dynasty could destabilize the region by bringing radicals or Islamists to power, or leaving a vacuum during a long power struggle.