Fatima Slutsker, a 57-year-old mother of two, died of wounds sustained when a rocket fell around 8:00 am (0500 GMT) in a street in the town of Sderot, five kilometres (three miles) north of Gaza, police and medics said.
A 24-year-old man was seriously wounded in the strike, one of six rockets to fall in Sderot in the morning hours, one of them not far from the house of Defence Minister Amir Peretz who lives in the town.
The man was a member of a private security firm that guards Peretz's home, police said.
In a statement, the defence minister vowed that the Jewish state would strike against those behind the rocket fire.
"These organisations will pay a heavy price," he said. "We will move against those who are involved in the firing of rockets, starting from their leaders and down to the last of their terrorists."
Wednesday's death marked the first time since July 2005 that Palestinian rocket fire killed someone inside the Jewish state, according to the army, and came a week after an Israeli artillery strike killed 19 Palestinians, mostly women and children, in Gaza's northern town of Beit Hanun.
In Gaza City, the armed wings of the Palestinian ruling Hamas movement and Islamic Jihad group competed with each other to claim responsibility for the strike, saying they had fired salvoes into Israel to avenge the Beit Hanun deaths, which sparked world-wide condemnation.
"This holy warrior operation comes... in response to the massacre of Beit Hanun and the continuing Zionist crimes against our Palestinian people," said a statement from Ezzedine al-Qassam Brigades, Hamas's armed wing.
"We stress that that our strikes against the enemy are continuing, and that for each (Israeli) shelling there will be a reprisal shelling, and that blood will be beget blood," it said.
But at a press conference held by five masked, armed members of the armed wing of Islamic Jihad said their gunmen were responsible for the strike.
"The enemy admitted he had been hit at 8:20 by two rockets, and that, thank God, they lead to the death of a Zionist and the injury of others," one of them said.
Following Wednesday's attack, Israel vowed that it would expand a four-month operation that it has conducted against militants in Gaza.
"The army has to launch a hard and unequivocal operation, even if we know that it can result in rocket fire, as this situation is intolerable," Eitan Cabel, minister without portfolio from the liberal Labour party told army radio.
Residents in Sderot, which has borne the brunt of rocket fire, echoed the calls.
"We have to reoccupy Beit Hanun and stay there as long as the strikes continue," said Naftali Timsit, 46, a deli owner.
"We live in fear," Rina Kalman, 35, said pointing to her house, whose windows were shattered by Wednesday's blasts.
Israel launched a massive offensive in Gaza on June 28, three days after militants there killed two soldiers and seized a third in a cross-border raid, with the aim of freeing the serviceman and halting the rocket fire.
More than 300 Palestinians and three Israeli soldiers have died inside Gaza in the offensive, the first time Israeli forces returned to the territory since withdrawing settlers and troops last year after a 38-year occupation.
A recent report by the Physicians for Human Rights group said that more than 60 percent of Palestinians killed in Gaza have been civilians and more than 20 percent minors.

Copyright AFP (Agence France-Presse), 2006