Ministry spokesman Ashraf al-Qudra told AFP that Ahmed Abu Habel, 15, succumbed to a head wound after being hit with a tear gas cannister fired by soldiers near a checkpoint between Israel and the Gaza Strip.
Israel's military did not comment on the specific incident but a spokeswoman told AFP that soldiers had "fired live rounds in accordance with the rules of engagement" as protesters massed along the border.
There have been months of demonstrations and clashes along the Gaza border. Wednesday's incident took place in the Beit Hanoun area of the northern Gaza Strip, near the Erez crossing into Israel.
At least 195 Palestinians in Gaza have been killed by Israeli fire since the protests began on March 30. One Israeli soldier has been killed in the border area over the same period.
Israel says its actions are necessary to defend the border and stop infiltrations and attacks, which it accuses Hamas, the Islamist movement that runs the Gaza Strip, of orchestrating.
Palestinians and rights groups say demonstrators have been shot while posing no real threat.
Israel and Palestinian militants in blockaded Gaza have fought three wars since 2008.
The protests have been calling for Palestinian refugees to return to their former homes now inside Israel.
More than 700,000 Palestinians fled or were expelled in the 1948 war surrounding Israel's creation.
Israel says allowing the so-called right of return would mean the end of the country as a Jewish state.
Last Friday, seven Palestinians, including a 12 and 14-year-old, were killed in clashes with Israeli forces along the Gaza border.
It was the bloodiest day of border protests since May 14, when more than 60 Palestinians died in violence accompanying the inauguration of the US embassy in Jerusalem, a move that enraged Palestinians.
The protests have seen Palestinians hurl stones and burn tyres. Israel says protesters have also targeted soldiers with explosive devices, grenades and gunfire, while infiltrations have been attempted.
Israeli snipers have been positioned on the opposite side of the fence.
The months of unrest have also led to several exchanges of rockets or mortars fired by Hamas and air strikes by Israel's military.
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