The three, a 14-year-old boy, and two men aged 45 and 50, were killed after a tank shell hit their house in Beit Hanoun in an attack that wounded four others, hospital officials said.
The Israeli army said the strike had targeted militants who had fired rockets at the Israeli city of Ashkelon north of Gaza in the morning.
"Two rockets were fired at Ashkelon, without causing casualties," an army spokesman said. "We identified those who fired the rockets and opened fire on them."
The radical Islamic Jihad group claimed responsibility for the rockets, saying it fired them in response to "the Zionist aggression against the Palestinian people and our brothers in Lebanon."
The rockets were fired at 8.15am, a quarter of an hour after a UN-brokered ceasefire between Israel and Hezbollah went into effect on the ground in Lebanon.
The deaths brought to 175 the number of Palestinians killed in Gaza since Israel launched a massive offensive on June 28, three days after Gaza militants killed two soldiers and seized a third in a cross-border raid.
One Israeli soldier has also been killed in the fighting, which the army says is aimed at recovering the captured soldier and stopping rocket fire from the strip into Israel.
Friday's fire came a day before the first anniversary of Israel's historic pullout from the coastal strip after a 38-year occupation.
At midnight on August 15, 2005, Israel began withdrawing 8000 Jewish settlers and thousands of troops from Gaza, the beginning of a month-long operation to end the Jewish state's occupation.
But a year on, Palestinians are bitter that the end of Jewish settlements did not bring an end to occupation or to the bloodshed.
"Israel portrayed this withdrawal as the Palestinians recovering their freedom and independence, but since the first day, the Gaza Strip has remained under occupation," said lawyer and rights activist Yunes al-Jaru.
"Many Palestinians hoped Gaza would become the embryo for an independent Palestinian state, but this hope has disappeared because of Palestinian leaders' inability to build (a state) and continued Israeli offensives," said Habib.
Since June 28, the Gaza Strip has been living and dying under the bombs, shells and missiles of the Israeli offensive.
Since then, the sealing off of the tiny, densely-populated territory has been almost hermetic. The only crossing point to the outside world, to Egypt in the southern town of Rafah, has been closed almost non-stop.
The situation has been worsened by economic sanctions imposed on the Palestinian government in the wake of Islamist faction Hamas's election victory in January.
Israel, the United States and the European Union consider Hamas a terrorist organisation because of its refusal to lay down arms or recognise Israel, leading to the suspension of much foreign aid to the Palestinians.
The withdrawal of Israeli forces was claimed as a victory by armed Palestinian groups, with a survey published last September showing that 84 percent of Palestinians considered the Israeli pullout "a victory for the armed resistance."
The settlers who were forced out of their Gaza homes, meanwhile, say that the withdrawal was a dire mistake that strengthened the resolve of Israel's enemies.
"Israel's flight from Gaza has opened the door for Hezbollah to attack," said Lior Kalfa, who chairs a committee for former settlers from Gush Katif, the largest settlement bloc in the Gaza Strip.
AFP