Medical sources identified al-Fayed, 42, as a senior commander from al-Quds Brigades, the armed wing of Islamic Jihad.
Two of al-Fayed's two children, a girl and a boy, were also killed in the blast, Palestinian doctors said.
"We will respond to this Zionist massacre painfully," Abu Ahmed, a spokesman for Islamic Jihad, said.
"We will strike the enemy everywhere."
Al-Fayed's house was completely destroyed, while several other houses in the neighbourhood were badly damaged.
At least 170 people, most of them fighters based in the Gaza Strip, have been killed since Israel and the Palestinians relaunched formal peace talks in November.
Israel is only pursuing negotiations with the Fatah faction led by Mahmoud Abbas, Palestinian president.
Fatah has been frozen out of the Gaza Strip since their forces were routed by rival group Hamas in June.