"An unmanned aerial vehicle (UAV) was identified penetrating Israeli airspace this morning, and was intercepted by the IAF at approximately 10:00 am (0800 GMT)," a military spokesman said.
Soldiers were searching the area where the drone was downed, in open areas in the northern Negev, to locate and identify it, the spokesman added.
Army radio said that the aircraft was not carrying explosives.
It quoted a military spokesman as saying troops responsible for monitoring "acted as they should have done after spotting the drone following its intrusion into Israeli airspace."
Military spokeswoman Lieutenant Colonel Avital Leibovich later told reporters: "This drone was spotted over the Mediterranean in a sector near the Gaza Strip before entering Israeli airspace, where the air force followed it."
"It was followed from the beginning until the time it was decided to intercept it and shoot it down for operational reasons over the Yatir Forest in the northern Negev, an uninhabited region."
Leibovich called the operation a "success", but she did not say how the drone was shot down.
"Israeli soldiers are at the scene and retrieving pieces of debris," she added.
The army dispelled the notion that the drone might have been launched from the Gaza Strip, and was looking into the possibility that Lebanese Hezbollah militants may have dispatched it, a military official told Israeli public radio.
The Ynet news agency said without quoting sources that "Hezbollah launched this drone. It is even possible that Iranians activated its launch and guidance system, and it is apparently of Iranian manufacture."
Ynet added: "The launching of such a craft over such a distance requires advanced means that Hezbollah does not possess up to now."
Asked about the reports by AFP, an army spokeswoman was unable to confirm or deny them.
In July 2006, the Israeli military shot down an unarmed drone operated by Lebanon's Shiite Hezbollah movement over the Jewish state's territorial waters.
And on April 12, 2005, another pilotless Hezbollah aircraft succeeded in overflying part of northern Israel without being downed.
