"Some kind of unmanned aerial vehicle (UAV) was spotted entering Israeli airspace from the Strip," an army spokeswoman told AFP.
"Fragments of it were later found in Israeli territory... right next to the (border) fence," she said.
She could not immediately say if the UAV was armed or fitted with a surveillance camera.
Hamas's armed wing has previously displayed a drone several metres in length and with the appearance of a small plane, though it was not immediately clear if Thursday's UAV was similar.
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There was no immediate claim of responsibility for Thursday's flight.
The Islamic militant group Hamas, the de facto ruler in Gaza, claimed responsibility for the drone incursions on July 14 and 17 last year.
They took place a few days after Israel launched a 50-day war against Hamas in Gaza which killed some 2,200 Palestinians, most of them civilians, and 73 on the Israeli side, most of them soldiers.