Five Palestinians, including a woman and seven-year-old child, died when the house in Rafah in southern Gaza was hit, and 15 other people were wounded, Gaza emergency services spokesperson Ashraf al-Qudra said.
Witnesses said the member, Abdel Razzaq al-Ghannam, was not at home when the attack happened.
An air strike around an hour before killed Anas Abu al-Kass, 33, of Gaza City's Tel el-Hawa neighbourhood.
According to Qudra, around 95 Gazans have been killed since Israel launched Operation Protective Edge early on Tuesday to halt cross-border rocket fire by groups in Gaza.
Since the start of the operation, Gaza fighters have fired 407 mortars and rockets that struck Israel, while another 118 rockets were intercepted by the Iron Dome missile defence system, an army spokesperson said Friday.
It is the deadliest violence since a November 2012 conflict in Gaza, and rockets have been fired at Jerusalem and Tel Aviv for the first time since then.
No Israelis have been killed from the rocket fire.
Israel has also authorised the call-up of 40,000 reservist troops, as it threatens a ground operation to stamp out rocket fire from attackers in Gaza.
Gaza rocket slams into Israel
A rocket fired from Gaza hit a petrol station in southern Israel on Friday, causing a huge explosion and injuring three people, the army and medics said.
"A barrage of rockets was fired at Ashdod, one of which hit a gas station causing massive damage," a statement from the army said.
Medics said three people had been taken to hospital, including one who was very seriously hurt.
"Three people were injured, one very seriously," emergency services spokesman Eli Bin told public radio of the incident, which occurred in the southern port city of Ashdod, 28 kilometres north of Gaza.
A large fire was raging at the site, with emergency teams trying to control the blaze, medics said.
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May Allah help these innocent people and destroy the enemies of humanity.strong text