Medical officials said the elderly woman was killed in the Israeli town of Sderot on Wednesday morning.
It is the first time since July 2005 that crude Palestinian rockets have killed an Israeli in the towns and villages that border the Gaza Strip.
Islamic Jihad, the armed wing of the ruling Hamas party, acknowledged responsibility for the attack, saying it had fired two rockets at Sderot.
Israel’s Channel 10 television said six rockets had hit the town around the morning rush hour.
Israel said it would respond.
David Baker, an official in the Israeli prime minister’s office, said: “Palestinian rocket launchers take aim at Israeli civilians. We will not tolerate such attacks and will take whatever steps are necessary to neutralise this threat.”
Emergency services said the rocket had hit a residential area.
The town is a frequent target for Palestinian rocket attacks.
Rockets had also fallen on a nearby Israeli village, but it was unclear if any were wounded in that attack.
The Israeli army has been carrying out repeated raids into Gaza.
Last week 19 Palestinians were killed in an Israeli artillery barrage on the northern Gaza town of Beit Hanoun, which borders Sderot.
Israel said the barrage was aimed at areas used by Palestinian fighters to fire rockets into Israel but went off due to a technical failure.