A 15-year-old boy was shot in the stomach during clashes with IDF forces east of the Jabaliya refugee camp, according to the Hamas Health Ministry on Friday.
According to the report, two other people were injured by gunfire in clashes with IDF forces east of Gaza City, when 9,000 demonstrators protested in five locations along the Gaza border.
A Palestinian was arrested after cutting the fence into Israel, waving a Palestinian flag.
The border protests began on March 30th and has seen over half a million people violently demonstrating along the security fence with Israel demanding an end to the 12-year long blockade, congregating at points along the border range between several thousand to 45,000 each day.
The one year anniversary of the border riots last week saw some 40,000 Palestinians demonstrate along the border fence and saw three Palestinians killed by IDF fire.
The cross-border violence immediately played into Israel's election campaign, which concluded earlier this week with Prime Minister Benjamin Netanyahu heading toward a record fifth term in office.
But Egyptian mediators intervened to avoid further escalation by persuading Israel to lift restrictions on the movement of goods and people in and out of Gaza and expand the breadth of Mediterranean waters where Gazans can fish.
The protesters are demanding an end to a blockade imposed on Gaza by Israel and Egypt, and want Palestinians to have the right to return to land from which their families fled or were forced to flee during Israel's founding in 1948.
Israel rejects any such return, saying it would eliminate its Jewish majority.
More than 200 Gazans have been killed by Israeli troops since the 'Great March of Return' started on March 30 last year, according to Gaza health officials. An Israeli soldier was also killed by a Palestinian sniper.
Last month's anniversary rally was smaller than expected, despite concerns that the event, during which four Palestinians were killed, would see a major escalation.
Israel seized Gaza in the 1967 Middle East War and pulled out its troops and settlers in 2005. It says its blockade is necessary to stop weapons reaching Hamas, which has fought three wars with Israel and fired thousands of rockets at it in the past decade.
Israel's use of lethal force at the border protests has drawn censure from the United Nations and human rights groups. U.N. investigators in February said Israeli forces might be guilty of war crimes for using excessive force.Israel says its troops have no choice because they are trying to stop militants breaching the fence and attacking Israeli communities nearby. Palestinians have also launched incendiary balloons and kites into Israel.Anna Ahronheim contributed to this report.