The niece, 38-year-old Zahadia Khaled Haniyeh, suffered a gunshot wound to her stomach while she was taking part in the protests on the border fence.
Her uncle came to visit her at the Al-Shifa Hospital in Gaza City on Saturday morning. He also visited other Palestinians wounded in the protests.
"The Palestinian people will continue with the marches despite the many wounded, until the land is purified of the filth of the occupation," Ismail Haniyeh said.
During the weekend, Fatah and Hamas representatives were in Egypt for talks in an effort to restart the reconciliation process between the two warring factions, after it had reached a dead end in recent months.
The UN's envoy to the Middle East Nickolay Mladenov, who also took part in the talks, said the Egyptian effort is beginning to bear fruit.
"Everyone is focusing on preventing the escalation and easing the suffering of the people, alongside reaching a political solution to the situation," Mladenov said.
Mohammed Abu Halima, 22, was killed in the protests on the Gaza border on Friday, as 3,000 Palestinians protested at five points along the border, with some rolling burning tires and throwing rocks.
The IDF said a number of terrorists attempted to approach the security fence with the intention of hurling an explosive device at soldiers adjacent to the Karni crossing in the northern Gaza Strip.
"The explosive device went off within the Gaza Strip and injured several Palestinians," the army said in a statement. "No injuries to IDF soldiers were reported."