Israel's Magen David Adom ambulance service said it was treating seven people, including an infant, a 3-year-old boy, a 12-year-old girl and a 60-year-old woman who was suffering from blast injuries, burns and shrapnel wounds.
There was no immediate claim of responsibility for Monday's incident.
The attack also comes 10 days after rockets were fired towards Tel Aviv.
The Jewish state will "respond forcefully" against Hamas after a rocket was launched from inside Gaza into Israel, Netanyahu said, according to local media. Seven people were wounded and the house was decimated.
Palestinian activists have been flying burning kites and balloons into Israel as part of ongoing anti-occupation protests along the Gaza-Israel buffer zone.
Emmanuel Nahshon, spokesman for Israel's Foreign Ministry, said the home in Mishmeret was hit by a rocket from Gaza.
Thousands protest in London to demand new Brexit vote
Independent legislator Chuka Umunna and others supporting a second Brexit referendum estimated the crowd at 1 million. The atmosphere was akin to that of a carnival as the masses thronged around central London ahead of the noon start.
Yahya Sinwar, the head of the Islamist militant group Hamas in the coastal enclave, canceled a planned public meeting scheduled for Monday afternoon, with Hamas officials citing "developments". Four family dogs were killed in the attack.
Israeli Prime Minister Benjamin Netanyahu, who is cutting short a trip to the United States over the incident, has vowed to respond with force.
Israel says the demonstrations are orchestrated by Hamas, which vocally supports them, sending free buses to the border and providing food and internet to participants - as well as money for those injured in them - in order to provide a cover for the organization's nefarious activities along the security fence, including infiltration attempts, the planting of explosives and attacks on Israeli soldiers. Trump tweeted that Israel should have full sovereignty over the long-disputed Golan Heights, which Israel seized from Syria during the 1967 Six-Day War. The territory is home to other armed groups, including Islamic Jihad, an Iranian-backed organisation that also has a formidable rocket arsenal.
The incident began when several Hamas prisoners stabbed two prison guards, moderately wounding one of them. Smaller flare-ups have occurred sporadically since Israel and Hamas fought their last war, in 2014.
Instead of a full-fledged conflict, Hamas has tried to end the blockade through a violent weekly protest movement along the Israel-Gaza border fence that it launched a year ago.
An Israeli police officer at the site of the attack.