Saif Abu Zaied was wounded in the head Wednesday and died at a hospital, the ministry said early Thursday.
The circumstances were not immediately known, but the incident occurred as dozens of youths engaged in “nighttime confusion,” a more violent form of protests involving firebombs and laser lights directed at Israeli forces along the border fence.
The night skirmishes are complementary to the weekly daytime protests that Gaza’s Hamas rulers have staged for a year.
The Islamic militant group wants an end to a crippling Israeli-Egyptian blockade on the Palestinian enclave.
On Wednesday, the Israeli military said a projectile was fired from Gaza and activated warning sirens in southern Israel.