Teenager Mohammed al-Jahjuh was "hit in the neck by a bullet (fired) by Israeli soldiers", ministry spokesperson Ashraf al-Qudra told AFP.
Israel destroys house of Palestinian charged with killing soldier
Abdelaziz Abu Sharia, 28, and Naher Yasin, 40, died from their wounds after being shot in separate incidents along the heavily fortified frontier with Israel, Qudra and a hospital official said.
The Israeli army said around 8,000 Palestinians had gathered at spots along the border, burning tyres and launching an incendiary device at soldiers that did not reach the troops.
Israel's military said it had opened fire "according to operational procedures" in place, without elaborating.
Forty six Palestinians - including two journalists and four first aid responders - were wounded, Qudra said.
Palestinians in the Gaza Strip have staged protests backed by Hamas since March 30.
At least 238 Palestinians have been killed since the protests began, mostly by Israeli fire during border clashes but also by air and tank strikes.
Two Israeli soldiers have been killed over the same period, one by a Palestinian sniper and another during an aborted special forces operation inside Gaza.
Israeli forces shoot dead Gaza teen during border protest
Protesters are calling for Palestinian refugees to be allowed to return to their former homes now inside Israel.
Israel accuses Hamas of seeking to use the protests as cover to carry out infiltrations and attacks, and says the army's actions are necessary to defend the border.
Israel has fought three wars with Hamas since 2008.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ