The ministry added that 17 other protesters were wounded.
The two teenagers were standing 50-60 meters (160-200 feet) from the fence at separate protests when they were shot by Israeli forces, according to rights group al-Mezan.
A military spokesperson said the demonstrators hurled rocks at Israeli troops and several explosive devices landed on the Gaza side of the fence.
Israeli security forces arrested a Palestinian man on Saturday suspected of killing an Israeli woman found dead two days ago in a forest on the outskirts of Jerusalem, police said.
A 19-year-old Israeli woman was stabbed to death as she walked through woods last week by a 'nationalist Palestinian, ' security forces say.
Since late March last year, the Palestinians in the Gaza Strip have been carrying out weekly protests, known as the Great March of Return, against Israel's 12-year crippling blockade on the coastal enclave.
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Trippier's short corner found the unmarked Christian Eriksen and he whipped a pin-point cross towards Sanchez six yards from goal. Replays showed the Colombia defender was just onside as he scored his first goal for Tottenham since his 2017 move from Ajax.
It added that the soldiers also killed Hamza Mohammad Roshdi Eshteiwi, 18, from Gaza city, after shooting him with live fire in the neck, east of Gaza.
Egypt has since eased Palestinian movement through its border and Israel allowed Qatar to send financial aid to Gaza, but the Hamas says this is insufficient.
At least 249 Palestinians have been killed by Israeli fire since then, the majority shot during clashes, though others have been hit by tank fire or air strikes.
The clashes along the border separating Israel and Gaza have led to periodic bouts of fighting over the past year, including Israeli airstrikes on the enclave and Hamas rockets fired at Israel. Protests have dwindled in recent months after an informal agreement between Israel and Hamas.
The suspect comes from the flashpoint city of Hebron in the south of the occupied West Bank, police said.