Leibovich did not give more details, but Israel media reported that the aircraft was not carrying explosives and could have been a surveillance drone.
Defense Minister Ehud Barak said in a statement that Israel views "this incident of attempting to enter Israeli airspace very severely and we will consider our response later," while Prime Minister Benjamin Netanyahu vowed that Israel "will continue to defend our borders in the sea, on the land and in the air for the security of the citizens of Israel."
It's not the first time that Israel has shot down a drone in its airspace, although such cases are very rare.
Hezbollah sent a few aircraft over Israel over the past decade but without much success. In the 2006 war, the militant group launched an Iranian-made drone capable of carrying explosives into Israel that was shot down. Another drone two years earlier crashed in the Mediterranean.
Last week Israeli authorities indicted an Arab citizen of Israel on charges of spying for Hezbollah, accusing him of gathering intelligence on security for Israel's president and other public officials as well as military installations.