At least another 12 people were injured, the ministry said, as Palestinians again demonstrated in different spots along the border. A spokesman said on Saturday he died from head wounds.
A number of Palestinians have been arrested, shot, or killed by Israeli forces for allegedly attempting to carry out attacks or being in possession of a knife at the Gush Etzion junction.
On September 5, the army said that hundreds of "rioters" had vandalised the Gaza side of the crossing, and that it would remain closed until the damage was repaired.
Since 2015, Palestinians have killed over 50 Israelis, two visiting Americans and a British tourist in stabbings, shootings and car-ramming attacks.
Israeli aircrafts targeted an observation point affiliated with the Ezzedine al-Qassam Brigades, the armed wing of resistance movement Hamas, which has governed the Gaza Strip since 2007.
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Islamic Jihad also praised the attack in a statement and described it "a natural response to the aggression and crimes that the Zionist terror perpetrates at the expense of the Palestinian people, land and holy sites", according to the Islamic Jihad-linked Palestine Today.
It says its actions are necessary to defend the border.
During last year's march by right-wing Israelis through East Jerusalem's Old City to mark 50 years since Israel seized control of it in the Six-Day War, Fuld said it was a "miraculous day" for Jews.
The suspected assailant was identified by his family as Khalil Youssef Jabarin, 17, from the village of Yatta in the southern West Bank.
The victim was identified as Ari Fuld, a USA -born activist who was well-known in the local settler community and an outspoken Israel advocate on social media platforms. Fuld, an American-Israeli resident of the Efrat settlement and a father of four, managed to chase down and shoot his assailant before collapsing.
He is then pursued by civilians and shot nearby.