It said he was evacuated for medical care Sunday and later succumbed to his wounds.
Earlier, it said three Palestinians armed with knives caught trying to cross the fence were detained for questioning.
There was no immediate comment from Hamas, the Islamic militant group that rules Gaza.
The Gaza border has been tense for months.
Hamas has led weekly border protests since March 30 aimed in part at drawing attention to the Israeli-Egyptian blockade imposed after it took control of the territory in 2007.
Since then, at least 128 protesters have been killed by Israeli fire and one Israeli soldier was killed by a Gaza sniper.
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