Faris Abu Hajaras, 26, was shot by Israeli fire in his stomach east of Khan Yunis Saturday and succumbed to his wounds Tuesday, the ministry said in a statement.
Tens of thousands of Palestinians gathered in different spots along the Gaza border Saturday for the first anniversary of the often violent protests there.
Four other men, including three 17-year-olds, were killed by Israeli fire Saturday, according to the ministry.
At least 263 Palestinians have been killed by Israeli fire since the protests and clashes began a year ago.
Two Israeli soldiers have been killed over the same period in Gaza-related violence.
Israel says its actions are necessary to defend its borders and accuses Hamas, the Islamist movement that rules the Gaza Strip, of orchestrating violence there.
But a UN probe has said Israeli soldiers intentionally fired on civilians in what could constitute war crimes.