Another five people were wounded in the raid against the home, which came just hours after the Israeli security cabinet gave the go-ahead for intensified operations against Palestinian militants.
The dead were all members of Khalil al-Hayya's family but he was away from his home in the eastern Al-Shujaya neighbourhood of Gaza City at the time of the attack.
The Israeli military confirmed there had been an air strike in northern Gaza but had no further comment.
Israel's Army Radio described Mr Hayya as a senior member of Hamas' military wing that it says manufactures and fires makeshift 'Qassam' rockets at Israel.
