The health ministry identified the man killed Thursday as Mohammed Abu Sharbin, 20.
The Israeli military said its forces fired toward several Palestinians who were seen approaching the fence and "sabotaging" it, without elaborating.
Gaza's Hamas rulers have recently scaled down a months-long wave of border protests as Egypt has been trying to mediate a truce between the Islamic militant group and Israel.
Israel says it is defending its border and accuses Hamas of using the protests as cover to stage border infiltrations and attacks.
More than 160 Palestinians have been killed in the demonstrations that began March 30. A Palestinian sniper shot dead an Israeli soldier in July.
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