"An (Israeli) fighter aircraft shot down a Hamas-owned unmanned aircraft flown from the Gaza Strip to the Mediterranean," an army spokeswoman said.
The drone fell into the sea without entering Israeli territory, she added.
"The Israeli army will not allow any violation of our airspace and will act firmly against any attempt of this kind," she added.
Hamas, with which Israel has fought three wars since 2008, did not immediately comment.
In December, Hamas accused Israel of the murder Mohamed Zaouari in Tunisia.
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