"Israel will take resolute and decisive measures to protect our citizens," government spokesman David Baker said. "We will not allow Israeli families to be victimized by Palestinian rockets in the heart of their own cities."
The rocket was one of 11 fired toward southern Israel on Saturday, police said. It landed yards away from a road where a family was running to seek shelter as warning sirens rang out to announce the attack, Israeli media reported.
A medic, who only gave his first name, Gil, said he heard a loud explosion and rushed toward the scene.
"I found two injured people, one boy very seriously wounded in the legs," the medic told Israel Army Radio. The younger brother's legs were at least partially severed by the explosion, Army Radio reported. Doctors told Israel TV that the same boy also was hit in the chest by shrapnel.
Their mother and a third brother were brought to the hospital suffering shock, medics told Channel Two TV.
The militant Islamic Jihad and Popular Resistance Committees groups claimed responsibility for firing rockets toward Sderot around the time of the attack.
Hours later, an Israeli airstrike on a car hit Palestinian militants in the southern Gaza Strip, killing one and injuring three, medics said.
Another airstrike targeted a training ground for Hamas militants. Earlier in the day, an Israeli airstrike on Palestinian militants launching rockets seriously injured one, medics said. Eighteen Palestinians, all militants except for one, were killed this week in Israeli strikes on the Gaza Strip.
Saturday's rocket attack on Sderot could put greater public pressure on Israeli Prime Minister Ehud Olmert's government to intensify measures to stop the rocket attacks.
The barrages have not abated despite Israel's withdrawal from the territory in 2005 and Israel's virtual-blockade of the territory in recent months, including a cutback in supplies of fuel and electricity through crossings that Israel still controls.
The Israeli army and government have been reluctant to launch a large military campaign in Gaza against the rocket operation for fear both soldiers and Palestinian civilians would suffer a great number of casualties.
On Saturday night in Sderot, residents burned tires at a major intersection, blocking roads. They demanded a military campaign in Gaza.
The rockets fall almost daily in southern Israel, occasionally causing casualties and instilling panic. Twelve Israelis have been killed by the rockets in the past six years.
Gaza militants had vowed to persist in their attacks despite an Israeli cutback on Thursday of about 1 percent of its power supply to the coastal territory that was meant to pressure the 1.4 million Palestinians there to get their Hamas rulers to stop the launchings.
Britain's Foreign Secretary David Miliband said Saturday in a statement that he was "extremely concerned" by Israel's reduction in electricity to Gaza, and urged Israel to reverse the decision. Miliband also called for a cessation of the rocket fire, and condemned a Hamas suicide bombing in Israel this week that killed one woman.
Israel has said it would not allow a humanitarian crisis to develop in the Gaza Strip.
Israel has imposed a near-hermetic blockade on Gaza over the past seven months, reducing all shipments into Gaza including fuel and some food items, following Hamas' violent seizure of the Gaza Strip from forces allied with moderate Palestinian President Mahmoud Abbas.
Israel has warned its partner in peace talks - Abbas' government - that it will not implement an agreement as long as serious violence continues. Abbas has no effective control of Gaza since the Hamas takeover.
