Leibovich said the operation was successful and the military was in control throughout.
"We had monitoring contact from the ground and from the air. We alerted jet planes that escorted the unmanned aerial vehicle and due to some operational considerations we decided to intercept the unmanned aerial vehicle in the northern Negev area, which has no population," Leibovich said.
It's not the first time that Israel has shot down drones entering its airspace, but such cases are rare. The Iran-backed Lebanese militia Hezbollah has launched several such aircraft into Israel over the past few years.
In the 2006 war, Hezbollah launched an Iranian-made drone capable of carrying explosives into Israel that was shot down. Another drone two years earlier crashed in the Mediterranean.
Israel and Iran are bitter enemies and tensions are high over Tehran's nuclear program, which the West believes is intended for atomic weapons. Tehran insists its atomic program is for peaceful purposes only.
Israel has hinted that military action should be taken to prevent Iran from getting nuclear bombs.
Leibovich would not elaborate how the unmanned vehicle was brought down. She said troops were searching for debris from the drone.
Defense Minister Ehud Barak congratulated the military.
"We view this incident of attempting to enter Israeli airspace very severely and we will consider our response later," he said in a statement.