The 40-year-old died after being shot in the chest near Khan Yunis in the southern Gaza Strip, while 18 people suffered bullet wounds in the protests, the ministry said.
The death takes to 53 the number of Palestinians killed since protests began on March 30 calling for Palestinians to be able to return to the homes they fled in 1948, which are now inside Israel.
Thousands of Palestinians gathered at five different points along the border, an AFP correspondent at the scene said.
Israeli forces responded with tear gas and live ammunition, according to Gaza's health ministry.
Israel's army said around 5,000 Palestinians took part in Friday's protest.
"The rioters burned tyres, threw stones at the security fence and Israeli soldiers" and also flew kites carrying incendiary devices to set fire to Israeli territory, the army said in a statement.
Israeli troops fired "in accordance with the rules of engagement," it added.
The army has been accused of using excessive force against protestors, with both the UN and EU calling for independent investigations.
The protests are due to culminate early next week.
On Monday, the United States is set to shift its embassy from Tel Aviv to Jerusalem and on Tuesday Palestinians will commemorate what they call the "Nakba", marking the creation of the state of Israel.
US President Donald Trump's recognition of Jerusalem as Israel's capital infuriated Palestinians, who see the eastern part of the city as the capital of their future state.
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