Ahmed Abu Hussein, 24, worked for Gaza's Al-Shaab radio station and wore a protective vest marked "Press" at the protest on April 13, witnesses said. Photos of Abu Hussein lying wounded in his vest appeared on social media.
He was the second journalist killed by Israeli gunfire since the weekly Friday protests, for a right of return of Palestinians refugees and their descendants to homes in what is now Israel, began on March 30.
The health officials said a bullet penetrated Abu Hussein's side. He was moved from Gaza to a hospital in the West Bank and then transferred to a hospital in Israel, where he died.
His death raised to 38 the number of Palestinians killed in the protests near the border.
An Israeli military spokeswoman had no immediate comment on Abu Hussein's death.
Yaser Murtaja, 30, a cameraman for Palestinian Ain Media, was shot on April 6 and died the next day. After his death, the Israeli military said it does not intentionally target journalists and that it would look into the circumstances of the shooting.
The Palestinian journalists' union accused Israel of "deliberately" targeting Abu Hussein and Murtaja, vowing to seek to bring "leaders of the occupation" to justice.
Abu Hussein will be buried in Gaza on Thursday.
Israel’s live-fire response to the protests has drawn international criticism.
Israel says it has been warning Gazans not to approach the border fence and that it is doing what is necessary to stop the barrier from being damaged or breached.
The Palestinians said Israel, which has deployed army sharpshooters along the frontier, used "excessive force against unarmed protesters". Some protesters have hurled stones and rolled burning tyres towards the fence.
Gaza is run by the Hamas Islamist movement, designated by Israel and the West as a terrorist group.