In a statement, the Israeli army blamed Hamas, the group governing Gaza, of "activities" that took place in the strip over the weekend, referencing the demonstration that had taken place near the fence with Israel.
The military said they had damaged the fence and were carrying an axe.
The 21-year-old volunteer paramedic died of a gunshot wound in Khan Younis, a city in the south, the Palestinian health ministry said.
The army circulated a picture of what it said was the axe lying on the ground near the border.
Palestinian protesters in Gaza have been flying flammable kites to set Israeli fields ablaze after Israeli troops responded with deadly force to weekly Friday protests on the border.
The latest death brings the number of Palestinians killed since then to 125.
A barrage of rocket and mortars into Israel from Gaza on Tuesday was followed by Israeli strikes on 65 militant sites in the Gaza Strip in the worst flare-up since the 2014 war.
No Israelis have been killed.
Protests peaked on 14 May when at least 61 people were killed as tens of thousands demonstrated ahead of Nakba Day, marking the 70th anniversary of the displacement of some 750,000 Palestinians during the establishment of the state of Israel in 1948.
Israel announced plans to deduct from tax funds it collects for the Palestinians to compensate Israelis living near the Gaza Strip who have fallen victim to a wave of arson attacks.
During a second vote, the United States failed to win support for its own rival measure calling on Palestinian militants to halt their protests in Gaza.
Last week, residents in Gaza attempted to break a 12-year crippling siege that has trapped more than two million Palestinians since 2006.
"With its veto, the United States is once again attempting to justify the lawlessness and cruelty of Israel's military occupation, while providing Israel with legal and political cover to pursue its assault on the Palestinian people and on worldwide law and global humanitarian law".
Israel withdrew its troops and settlers from Gaza in 2005, but maintains a tight blockade since 2007.
Egypt also restricts movement in and out of Gaza on its border.