An army statement said troops thwarted an "infiltration attempt" by "two terrorists who damaged the security fence and were armed with an axe."
Soldiers "fired towards the terrorists, killing one of them," it added, without clarifying what happened to the second suspect.
There was no immediate confirmation from the health ministry in Gaza.
The death brings to 125 the number of Palestinians killed by Israeli fire in Gaza since March 30.
Israeli army kills 21-year-old Palestinian nurse in Gaza border protest
The vast majority have been killed during weeks of protests along the border.
Protests peaked on May 14 when at least 61 people were killed as tens of thousands approached the heavily fortified border in a demonstration coinciding with the controversial opening of the US embassy in Jerusalem.
On Friday a 21-year-old female medic was shot dead in southern Gaza.
No Israelis have been killed.
The Jewish state accuses Gaza's extremists Hamas of using the protests as an excuse to carry out attacks.
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