While the pilots of the jet survived by waiting until they re-entered Israeli airspace before ejecting, the attack has nonetheless sparked concern.
A convoy of missile-defence batteries has headed north towards the border region with Syria, Israeli media has reported, while witnesses have posted photos on social media of military trucks making their way towards the town of Baka al-Gharbiya.
The Israel Defence Forces have not commented on the deployment.
The drone was then shot down by an Israeli helicopter.
A security official said: “The squadron was sent to protect the country’s skies. We identified the aircraft as an Iranian drone, and when it crossed the border, we shot it down into Israeli territory.
“The squadron is ready and prepared for any task it is given.”
In response to the incursion, Israel sent eight jets to attack the drone’s launch site in Syria.
But the jets were targeted with 20 anti-aircraft missiles and one jet was destroyed.
An IDF spokesman said: “Iran has been using the base in recent months for the purpose of transferring weaponry to be used against Israel.
“These actions by Iran at the base are ostensibly carried out under the guise of supporting the fighting against the global Islamic jihad forces, but the actions carried out in the past 24 hours prove that its real concern is direct, violent action against Israel.
“In the Iranian action, all the Israeli warnings against Iranian consolidation in Syria were realised.
“The attack was initiated and Israel was forced to respond first to the threat in its territory and then to the hostile elements operating from the Syrian territory opposite it.”
Another source said: “As far as we are concerned, the event is over but the Iranians are determined to continue to establish themselves in Syria; the next incident is only a matter of time.
“We do not know what the mission of the Iranian drone was. It is their most advanced drone and they did not expect our radar to detect its penetration into our territory. Our aerial freedom will not be harmed. We will continue to destroy targets.”