The aircraft crashed in the north of the Negev desert. It is not clear where it came from.
Military officials said the aircraft had flown in from the west, but not from the Gaza Strip.
The army said it was unclear if the drone was being used for reconnaissance or for a potential attack.
However, Israeli radio quoted a military spokesman as saying the aircraft was not carrying explosives.
Military spokeswoman Lt Col Avital Leibovich said the drone, which flew over the Gaza Strip but did not originate from there, had been detected by Israeli ground systems.
She said Israeli jets flew alongside the aircraft before deciding to bring it down in the largely uninhabited northern Negev area.
Other officials said the drone had spent about 20 minutes in Israeli air space.
Defence Minister Ehud Barak said Israel viewed the incident "very severely".
"We will consider our response later," he added, raising the possibility of retaliatory action.
Correspondents say small drones have penetrated Israeli territory in the past, but from the north.
On at least three occasions unmanned aircraft operated by the Lebanese Shia movement Hezbollah were detected.
In November 2004, Hezbollah's military wing briefly flew a drone over northern Israel on a surveillance mission. Drones were also launched in April 2005 and on 7 August 2006, a day before the end of the month-long war between Israel and Hezbollah.
During the 2006 conflict, the Israeli Navy corvette INS Hanit was struck by a shore-launched missile. It is understood to have been an Iranian-built Noor - a clone of the Chinese C-802 radar-guided anti-ship missile.
The Israeli air force has shot down a small unmanned aircraft after it entered the south of the country, the military has said.