Muawiya Hassanin, head of Gaza's emergency services, said the man was Salim Jumaa al-Hamedi, aged 18.
Two missiles were later fired from northern Gaza into the Israeli town of Sderot, in an attack claimed by al-Aqsa Martyrs' Brigades.
Abu Qusai, a spokesman for the group, said the rockets were fired in retaliation for the killing of its one of its fighters in Gaza and the death of one of its members in the West Bank town of Jenin a day earlier.
The Israeli police said no damage or injuries were reported after the rocket attacks.
Hamas, which has de facto control of Gaza, said on Thursday it had arrested two fighters who fired the rockets, the first such occurrence since the truce took hold.
A truce between Israel and Palestinian armed groups in Gaza – including ruling organisation Hamas – has been in place since June 19.
Both sides have accused each other of violating the terms of the ceasefire deal in recent weeks.
West Bank killing
The shooting in Gaza and the rocket attacks come a day after Israeli security forces shot and killed a Hamas member in the occupied West Bank.
Israeli troops shot the man as he tried to escape arrest near the town of Jenin on Wednesday, the Israeli army said.
"The operative, Talal Sa'ad Talal Abed, was initially critically wounded and received medical treatment at the scene, but died on the way to a hospital," an Israeli army statement said.
"Abed, 32, a resident of Kafr Dan, was a member of Hamas's terror infrastructure in the village, an infrastructure that attempted to dispatch a suicide bomber into Israel.
"After the failed attempt, cell members were arrested by Palestinian security forces. Despite this, the group continued to be involved in terror, and had been planning an imminent terror attack."