The 14-year-old was named as Hassan Shalabi, the son of a niece of Ismail Haniyeh, the political chief of Hamas.
The military said it was aware of reports that a protester had been killed but could not confirm that the individual was a 14-year-old or what caused the death.
About 7,000 people were protesting at several points along the fense, the military said, adding that protesters were clashing with troops and that some had thrown explosive devices and grenades that landed on the Gaza side of the fence.
It was the 46th Friday protest in a row.
On Sunday, the Gaza Health Ministry said that Ahmed Abu Jabal, 30, succumbed to bullet wounds sustained on the Gaza border the previous week.
During last Friday’s weekly protest, 32 Palestinians were wounded by Israeli live fire according to Gaza authorities.
According to data in a United Nations report released last month and confirmed by Israeli security officials, 295 Palestinians were killed and about 6,000 wounded by live ammunition since protests began last March.