An Israeli warplane shot down a "suspicious object" flying on Dec. 16 over the southern part of the Dead Sea, the military said, adding that the intruder appeared to have been a balloon.
The country's main nuclear reactor is about 20 miles from the Dead Sea, at Dimona in the Negev desert.
"Air force planes were scrambled after a suspicious object was seen," a military spokeswoman told AFP. "It was shot down." She did not elaborate.
Local news site Ynet said one of the planes fired a missile at the object "which was hovering close to the nuclear research institute at Dimona."
It said the balloon appeared to be powered by an engine, but was unmanned.
Aircraft are forbidden from flying over the reactor near Dimona.
Israel says the reactor is for research purposes, but defense analysts say it is the centre of Israel's undeclared nuclear weapons program. They say Dimona has been used to produce up to 200 nuclear warheads.
The Dimona plant was built with French aid at the beginning of the 1950s.
But Israel has never confirmed or denied reports that it has produced nuclear warheads.
Israel is not a signatory of the nuclear Non-Proliferation Treaty (NPT) and refuses to submit its nuclear facilities to inspection by UN watchdog the International Atomic Energy Agency.