In response, an Israeli aircraft hit two Syrian army tanks and a heavy-machine-gun position on the Syrian side of the buffer zone that separates the two countries, the spokesman said.
The Israel Defense Forces released aerial video of the airstrikes. The spokesman did not say whether the errant fire from Syria consisted of mortar rounds, artillery shells or bullets.
Syrian media reported that at least two people were killed as a result of the Israeli strikes on the outskirts of the Syrian farming town of Quneitra, which is visible from the Israeli side and has been a scene of frequent clashes in the six-year conflict between anti-government forces and the Syrian army.
Syria's state news agency, quoting a Syrian army communique, alleged that the Israeli strikes coincided with an attack by militants in the area and suggested that Israel was aiding the Islamist forces, according to Reuters news agency.
Prime Minister Benjamin Netanyahu said the Israeli retaliatory strike "made our policy clear: We are not willing to accept any spillover or leakage of fire from any front. We will respond with force to any fire on our territory."
On Saturday, Israel lodged a complaint about the errant fire to the U.N. Disengagement Observer Force, a peacekeeping mission operated by international troops that monitors the 1974 buffer zone between Israel and Syria.