The house, which was partly destroyed by the force of the blast, belonged to Abu Yusuf Kuka who heads the Palestinian Popular Resistance Committees' armed wing - the Victorious Salah al-Din Brigades.
The organisation mainly consists of former supporters of Palestinian Yasir Arafat's Fatah movement.
The group said Kuka was not wounded and that the three moderately injured Palestinians were members of the Brigades.
It accused Israel of having fired the rocket from the nearby sea.
However, an army spokesman declined to comment on the incident.
Palestinian police cordoned off the area after the blast in Gaza City's Shaati refugee camp.