Ministry spokesman Ashraf al-Qudra told AFP that Abdul Qadir Farhat, 19, died "after he was shot directly in the head by the military in clashes close to the Beit Hanoun (Erez) crossing" in northern Gaza.
He added that around 30 others were wounded, "among them 14 shot with live ammunition", and were moved to hospitals across Gaza.
Some were being treated for exposure to tear gas, he added.
Hundreds more have been wounded in clashes with Israeli forces.
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Seven Israelis have been killed and dozens wounded in a series of gun, knife and car attacks.
The Gaza clashes occurred during what Palestinians called a "Friday of revolution" against Israel.
Hundreds of demonstrators clashed with the Israeli military at different locations across Gaza after Hamas and Islamic Jihad called for protests.
Violent protests that first began in annexed east Jerusalem and the occupied West Bank have spread to Gaza in recent days.