The Ministry of Health spokesperson, Ashraf al-Qidra, said that Ahmed Abu Abed died late on Tuesday.
"Ahmed Abu Abed, aged four years and eight months, died as a result of the wounds he received last Friday east of Khan Younis," al-Qudra said in a statement on Tuesday.
He said Abu Abed was injured by shrapnel when his father was shot during regular Friday protests, dubbed the Great March of Return.
The boy's funeral will take place on Wednesday.
The killing of four-year-old Abu Abed follows months of demonstrations by Gazans along the fence with Israel, demanding their right to their ancestral lands from which they were expelled 70 years ago.
The Great March of Return rallies culminated on May 15 to mark what Palestinians refer to as the Nakba, or Catastrophe - a reference to the forced removal of 750,000 Palestinians from their homes and villages to clear the way for Israel's establishment in 1948.
So far, more than 195 Palestinians have been killed in Gaza, one of the most densely populated places on earth.