It is unclear which of the many groups fighting in Syria may have planted Tuesday's bomb. But Israel has said it holds Assad responsible for any attacks emanating from his country, and accused his forces of allowing the attack to take place.
"Our policy is clear. We hurt those who hurt us," Prime Minister Benjamin Netanyahu said. Defense Minister Moshe Yaalon said Assad would "regret his actions" if attacks continue.
Israel captured the Golan Heights, a strategic plateau overlooking northern Israel, from Syria in the 1967 Mideast war. It later annexed the area, though that move is not internationally recognized.
Gunfire and mortar shells from the fighting in Syria have occasionally landed in the Golan in recent years. Israel has said much of the fire was errant, but has responded with artillery fire in several cases. None of those reprisals, however, were as intense as Wednesday's airstrikes.
The Israeli military said its warplanes hit a Syrian army training facility, an army headquarters and artillery batteries. Israel also had carried out artillery strikes against Syrian military targets shortly after Tuesday's bombing.
The Syrian military said the raids early Wednesday targeted three army posts near the town of Quneitra, on the edge of the Israeli-occupied part of the Golan. It confirmed the death of one soldier and said seven were wounded.
The Syrian army denounced the airstrikes as Israel's "desperate attempt to escalate and worsen the situation" and to divert attention from Damascus' advances on the battlefront, especially the military's capture last weekend of a key rebel stronghold near the Lebanese border.
"Repeating such hostile acts (airstrikes) would endanger the security and stability of the region and make it open to all possibilities," a Syrian military statement said.
Analysts said they did not expect the situation to deteriorate, since neither Israel nor Syria is interested in a full-fledged war. Assad is focused on his battle against the rebels and Israel has little desire to upset a period of relative quiet. Syria's ally, Hezbollah, possesses tens of thousands of rockets and missiles aimed at Israel.
Even so, the area has seen an increase in tensions in recent weeks.
Last week, a roadside bomb exploded near an Israeli military patrol along the Lebanese border, causing no injuries. Israel responded with tank and artillery fire at suspected Hezbollah targets in southern Lebanon.
Earlier this month, the Israeli army said it killed two militants affiliated with Hezbollah — whose forces are fighting in Syria alongside Assad's troops — as they were trying to plant a bomb along the frontier.
Also, an Israeli airstrike last month reportedly targeted a suspected Hezbollah weapons convoy in northeastern Lebanon, though officials in Israel never confirmed it. Hezbollah said it would retaliate for the airstrike, which killed a Hezbollah official overseeing the operation.
Israel stopped short of blaming Hezbollah outright for Tuesday's bombing, but defense officials said the group remained the main suspect.
Israel and Hezbollah are bitter enemies. They fought a monthlong war in 2006 that ended in a stalemate, and both sides have been gearing up for another confrontation.
Israel has said it will not allow sophisticated weapons to flow from Syria to the Iranian-supported Hezbollah. Since the Syrian war broke out, Israel has carried out a series of airstrikes in Syria that destroyed weapons shipments believed to be headed to Hezbollah.
While the Israel and Syria have largely refrained from direct confrontation since the 1973 Mideast war, Israel has shown a readiness to act.
In 2007, Israeli warplanes bombed a suspected nuclear reactor in Syria, and on two previous occasions, Israeli warplanes buzzed over Assad's palace in a show of strength. In 2003, Israel also bombed a training camp belonging to a Syrian-backed militant group that had carried out a suicide bombing in Israel.
Israel also remains concerned that an ouster of Assad could see power in Syria fall to Islamic militants there, particularly al-Qaida-linked groups, and further destabilize the region.
Israeli analyst Ephraim Kam said neither Syria nor Israel want war, and that Hezbollah and Israel are interested in only limited confrontations.
"What can Israel achieve by going to war?" asked Kam, a researcher at the Israeli Institute for National Security Studies. "Syria is not in a position to go to war now, with civil war taking place."