"These events in Syria compel the world to take action, not just talk, but action. These are crimes against humanity and the international community must not stand on the sidelines," Barak said in a speech at the Institute for National Security Studies in Tel Aviv.
An army commander said separately that the Israeli military was making preparations along its border with Syria in case Assad's government collapsed, an event which he said could provide Islamist militants with a "warehouse of weapons" and a new operating base.
"Syria is in civil war, which will lead to a failed state, and terrorism will blossom in it," Major-General Yair Golan told a conference at Bar Ilan University. "Syria has a big arsenal."
Although Israel and Syria are technically at war, Israeli leaders have rarely censured the Assad government for its domestic crackdowns and initially said little about the uprising that erupted last year against Assad.
The Syrian leader is widely viewed in Israel as emulating his late father, Hafez al-Assad, in seeking to maintain decades of calm along a ceasefire line on the Israeli-occupied Golan Heights, captured from Syria in a 1967 war.
Barak welcomed the expulsion on Tuesday of Syrian diplomats from at least seven Western capitals, describing it as a "very important step in the right direction" after the killing of more than 100 civilians in the Syrian town of Houla.
But he said: "I don't think that Assad lost an hour's sleep last night because of those people leaving.. and more concrete action is required."
Barak did not specify what additional steps he wanted the West to take.
Major-General Golan, commander of Israeli forces on the border with Lebanon and the frontline with Syria in the Golan Heights, told an audience at the Begin-Sadat Centre for Strategic Studies that the situation in Syria put Israel at risk.
It was difficult to forecast how Syria would break up, Golan said. It could be effectively "cantonised" by the conflict.
The Israeli army was "deeply engaged in getting ready, with plans and physical means" along the borderlines, he said, without offering details.
Syria's stock of mainly Russian-made weapons includes surface-to-air missiles, surface-to-surface missiles and marine missiles. It also possesses chemical weapons which Syria never used in its wars against Israel but which could be attractive weapons for terrorists, the general said.
Golan said Assad's ally Iran was trying hard to help him stay in power and Iran's Lebanese ally Hezbollah is in turn a very determined enemy of Israel which has "no intention of letting us off easily".
Hezbollah is the most potent hostile military force directly on one of Israel's borders but it has done nothing evident in the past 14 months to exploit the Syrian crisis or start trouble with Israel to divert attention from Assad's crackdown.