The victim was identified as Faris Meqdad, 18, ministry spokesman Ashraf al-Qudra said.
Egyptian forces have previously opened fire on Gazans they accused of crossing the maritime border between Egypt and the Palestinian enclave.
Jihadist fighters have been battling Egyptian forces in Egypt's Sinai peninsula, which borders Gaza. Egypt rarely opens its border with Gaza, and the strip also faces an Israeli blockade.
Since the ouster of its Islamist president Mohamed Morsi in 2013, Egypt says it has destroyed hundreds of tunnels used to transport militants, merchandise and arms between the Gaza Strip and the Sinai Peninsula.
In September, Hamas accused Egypt of further besieging the Gaza Strip by flooding the border area to the south.