Health ministry spokesman Ashraf al-Qudra said Mohammed Abu Halima, 22, had died from shrapnel wounds to his chest, sustained in an explosion east of Gaza City.
Qudra could not provide AFP with details on the source of the shrapnel.
But Palestinian eye witnesses said Abu Halima was wounded when a device he was holding exploded.
The Israeli army said that "a number of terrorists attempted to approach the security fence with the intention of hurling an explosive device at IDF soldiers adjacent to the Karni crossing in the northern Gaza Strip".
"The explosive device went off within the Gaza Strip and injured several Palestinians," the army said in a statement. "No injuries to IDF soldiers were reported."
Some 3,000 Gazans took part in weekly demonstrations and clashes along the border with Israel on Friday, according to a military spokeswoman.
Qudra said 146 Palestinians had been injured in the day's protests, most of them from tear gas and 24 by Israeli gunfire.
Palestinians in Gaza have been demonstrating against Israel's decade-long blockade of the territory and in support of their right to return to lands they fled or were driven from during the war surrounding the creation of Israel in 1948.
Since the protests and clashes broke out along the Gaza border on March 30, at least 139 Palestinians have been killed by Israeli fire.
The majority were involved in protests and clashes, but others were seeking to breach or damage the border fence.
No Israelis have been killed.
Israel says its use of live fire is necessary to defend its borders and stop infiltrations. It accuses Gaza's Islamist rulers Hamas of seeking to use the protests as cover for attacks.
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