Ministry spokesman Ashraf al-Qodra identified the teenager as 16-year-old Abdel Rahman al-Dabbagh, and said he was killed east of Bureij refugee camp in central Gaza.
Witnesses said a group of young Palestinians gathered near the security barrier between Israel and the Gaza Strip and threw stones at Israeli lookout towers, prompting soldiers to open fire.
Qodra said the teenager was hit in the head and taken to hospital where he was pronounced dead.
The border region between Israel and Gaza is the scene of near weekly Friday confrontations.
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Israel and Palestinian militants in Gaza have fought three wars since 2008 and there are frequent flare-ups along the border.
Israel regularly responds to rocket fire from militants in Gaza with air strikes.
Last month, it carried out dozens of strikes in Gaza in response to rocket fire, a greater response than usual.
The Gaza Strip is run by the Islamist Palestinian movement Hamas.
It has been under Israeli blockade for around a decade and its border with Egypt also remains largely closed.
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