The rocket from the Palestinian enclave and expected Israeli response comes at a highly sensitive time just ahead of Israel's April 9 elections.
Israel's army said the rocket was fired by Hamas, the Islamist movement that runs the Gaza Strip, from the Rafah area in the south of the enclave.
It announced it was sending two additional brigades to reinforce the Gaza area and said it was carrying out a limited call up of reservists.
Netanyahu, currently in Washington, said he would return home after meeting US President Donald Trump later Monday, cancelling an address to pro-Israel lobby AIPAC's annual conference on Tuesday.
Israel also closed its people and goods crossings with the blockaded Gaza Strip and reduced the zone in the Mediterranean it allows for Palestinian fishermen off the enclave, a statement said.
The house hit was located in the community of Mishmeret, around 20 kilometres (12 miles) north of Tel Aviv, police said.
The rocket would have had to travel some 120 kilometres (75 miles) from Rafah to hit the house in the community of Mishmeret.
Rocket fire from Gaza at that distance is rare.
The hospital treating the wounded said seven Israelis were injured lightly by burns and shrapnel, including three children.
One of the wounded was a six-month-old child and six of them were members of the same family.
The house was destroyed in the wake of the rocket and subsequent fire, with burnt wood, a children's toy and other debris piled at the site.
Islamic Jihad warning
Police spokesman Ami Ben David said air raid sirens wailed at around 5:15 am and the home's residents made their way to a safe room, possibly saving their lives.
The rocket crashed through the roof and then exploded when it hit the floor, he said.
Netanyahu said "there has been a criminal attack on the state of Israel and we will respond with force."
"I will meet President Trump in a few hours and just after that I will return to Israel to lead closely the operations," he said in a video released by his office.
There was no immediate response from Hamas but its ally in Gaza, Islamic Jihad, said "we warn the Zionist enemy from committing an aggression against the Gaza Strip".
"Their leaders should be aware that we will respond with force against their aggression," it said, without commenting on who may have been responsible for the rocket.
The rocket comes after mounting tensions in recent weeks.
Netanyahu is believed by many analysts to want to avoid another war in the Gaza Strip -- the fourth since 2008 -- with unpredictable results ahead of the elections.
But he faces a tough challenge from a centrist political alliance led by former military chief Benny Gantz and he was already coming under heavy political pressure to react firmly.
Gantz asked on Twitter, in a reference to corruption allegations against Netanyahu, whether the prime minister would "finally focus on the security of the citizens of Israel instead of dealing only with his legal concerns."
Monday's incident comes after two rockets were fired from Gaza towards Tel Aviv -- also rare -- on March 14.
No damage or injuries were caused, but Israel responded to that and further rocket fire by hitting what it said were around 100 Hamas targets across the Gaza Strip.
Four Palestinians were reported wounded in those strikes.
Both Hamas and Islamic Jihad denied they were behind the March 14 rocket fire towards Tel Aviv, raising the possibility they were launched by fringe groups.
Israel's military said they were launched by Hamas, but later there were Israeli media reports that the army's preliminary assessment was that they had been fired by mistake during maintenance work.
The reports were a sign that Israel was seeking to calm tensions. The military refused to comment on the reports at the time.
Monday's rocket comes just days ahead of the first anniversary on March 30 of Palestinian protests and clashes along the Gaza Strip's border with Israel.
An informal truce between Hamas and Israel had led to relative calm along the border, but recent weeks have seen another uptick in violence.
Netanyahu's visit to the United States was expected to include Trump's formal recognition of Israeli sovereignty over the Golan Heights, which it seized from Syria in the 1967 Six-Day War.
Breaking with longstanding international consensus, Trump said last week that the United States should recognise Israeli sovereignty there.