Israeli and Palestinian security sources said the shootout occurred early on Monday.
“A Palestinian gunman opened fire along the Gaza border. Soldiers arrived at the scene and exchanged fire with him. We identified a hit,” a spokeswoman for the Israeli army said.
It was not immediately known if he was affiliated to a resistance group.
Israel pulled out its settlers from the Gaza Strip last autumn but has retained control of the Palestinian territory’s borders, sea and air space.
The Palestinian was the third fighter to be killed by Israeli forces in two days.
On Sunday, soldiers killed two Palestinian fighters during a raid in the West Bank city of Bethlehem. A third was arrested.
Palestinian sources initially said the two killed in Bethlehem were members of the security forces.
They later confirmed the army’s account that they were with al-Aqsa Martyrs Brigades – an armed offshoot of the Fatah movement headed by Mahmoud Abbas, the Palestinian president.