Muhamed Suleiman Atiyya was killed after evening prayers on Thursday in the southern Gaza town of Rafah.
The AFP news agency reported that shortly afterwards a Hamas member of the interior ministry security force was injured when two hand grenades were thrown outside a Rafah hospital.
Earlier, a Hamas member had been shot and wounded in Beit Lahiya, in the northern Gaza strip.
The Palestinian territories have seen a surge in internecine violence between Hamas and Fatah in the past week.
At least 14 people have died and over 100 injured in the worst internal bloodshed since the creation of the Palestinian Authority in 1994.
The violence follows a breakdown in negotiations between the two groups to form a national unity government.
Despite pressure from Western governments, Hamas has refused to accept a political programme that amounts to recognition of Israel and past Israeli-Palestinian agreements.
On Wednesday, two Palestinian activists were killed in an Israeli missile attack on their car in southern Gaza, according to witnesses.
Witnesses said the two, Yasser Ashur Abu Atim and Mohammed Zaqzuq, were members of the armed wing of Islamic Jihad.
The men were driving in Rafah near the border with Israel when their car was struck by at least one missile from an Israeli aircraft, the sources said.
In another incident late on Wednesday, a member of the armed wing of Hamas was wounded in a clash with armed men at Khan Yunus in the south of the Gaza Strip, witnesses said.