The Israeli military also said it filed a complaint through United Nations forces operating in the area, stating that "fire emanating from Syria into Israel will not be tolerated and shall be responded to with severity."
Israeli defense officials said the incident was not considered a serious military threat, but Israel felt the need to respond in order to set clear limits for the Syrians.
Defense Minister Ehud Barak said Israeli defense forces have been instructed "to prevent the battles from spilling over into our territory."
"Additional shelling into Israel from Syria will elicit a tougher response; exacting a higher price from Syria," Barak said.
Nineteen months of fighting and the mounting chaos engulfing the Assad regime have already shaken the region, spilling into Lebanon, Turkey and Jordan. In new violence Sunday, Syrian army forces backed by helicopter gunships and artillery attacked a border area with Turkey after rebels captured a crossing point, activists said.
The Syrian Observatory for Human Rights, a Britain-based activist group, said the Ras al-Ayn border area in Syria's northeast was "under siege" as dozens of rebels tried to hold onto the border crossing.
The entry of Israel into the fighting would take the violence to a new level. Although Israel has a more powerful military, both countries have air forces and significant arsenals of tanks, missiles and other weapons. Israel is especially concerned about Syria's stockpile of chemical weapons.
An Israeli war on Syria could also draw in Syria's ally, Hezbollah, further destabilizing the region. Hezbollah, which possesses tens of thousands of rockets and missiles, battled Israel to a stalemate during a monthlong war in 2006.
On Israel's southern flank, Hamas militants in the Gaza Strip, who battled Israeli forces over the weekend, might also enter the fray.