Saheeb Abu Kashef, 16, died late Saturday after being shot on August 3 east of Khan Yunis in the southern Gaza Strip, according to the ministry.
At least 180 Palestinians in Gaza have been killed since protests and clashes erupted along the border on March 30.
One Israeli soldier has been killed since then.
Israel accuses Hamas of seeking to use the protests to carry out attacks or infiltration.
It says its actions are necessary to defend the border.
Palestinians and rights groups say protesters have been shot while posing little threat.
Israel and Hamas have fought three wars since 2008.
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