Yussef al-Daya, 14, was hit in the chest to the east of Gaza City, ministry spokesman Ashraf al-Qudra said, AFP reported.
Around 30 other Palestinians were wounded by Israeli fire in rallies along the frontier, he added.
The Israeli army said around 8,000 Palestinians demonstrated at various points along the border, without commenting on the teenager's death.
The protesters set tires ablaze and threw grenades, incendiary devices and stones towards Israeli soldiers, an Israeli army spokesperson said.
At least 251 Palestinians have been killed by Israeli fire since March 2018, the majority shot during weekly border protests and others hit by tank fire or airstrikes.
Two Israeli soldiers have been killed over the same period.