A spokesman for the Hamas Health Ministry said Bilal Auwaida died when he was shot in the chest near Beit Lahiya in northern Gaza, the New York Times reported Friday.
A second man was wounded.
In a separate incident, Palestinian spokesman Ashraf al-Qedra said five people were wounded as about two dozen people demonstrated east of the Jabaliya refugee camp.
The protest was in support of farmers who have fields near the fence that marks the boundary between Israel and the Palestinian territories.
An Israeli military spokeswoman said one shot was fired at each location after soldiers fired warning shots to disperse the crowd, which had damaged the fence, hurled stones and rolled burning tires at the soldiers.
Violence along the border has increased during the past week, with the Israeli military twice targeting suspected militants. Over the past several weeks, Palestinian rockets have been fired into Israel from Gaza, at one point causing some schools to cancel classes.
The attacks did not cause any injuries or damage.