Mohammed Abu Zaida, 18, was shot in the neck and Mohammad Qita, 26, was hit in the stomach, ministry spokesman Ashraf al-Qudra said.
Fifteen other Palestinians were wounded by Israeli fire during the clashes east of the Bureij refugee camp in central Gaza, he said.
The Israeli army confirmed it had fired on protesters after they breached the "buffer zone" along the border.
"Dozens of rioters have breached the buffer zone and are attempting to damage the fence," a spokeswoman said.
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Israel and the Palestinian territories have seen a wave of violence in recent months, with 23 Israelis and 154 Palestinians killed since October 1.
Most of the Palestinians have been killed carrying out attacks, while others were shot by Israeli forces during protests and clashes.
An American and an Eritrean have also died in the violence.
Fridays are known as a day of protest across the Palestinian territories.