The woman, Shir-El Friedman, was standing next to the car at the time of the strike and was taken to Barzilai Hospital in Ashkelon. Hospital spokeswoman Lea Malul said she died on the way to the hospital.
The two wounded individuals, one of whom was moderately hurt and the other lightly injured, were also evacuated to Barzilai Hospital, along with twelve others who suffered from shock.
Hamas, Islamic Jihad, and the Popular Resistance Committees all claimed responsibility for the attack.
This is the first fatality in an unrelenting barrage of rockets fired at Sderot and the western Negev in recent days, which has caused widespread damage and left several other people wounded.
The last Israeli fatality in a Qassam rocket attack, 43-year-old Yaakov Yaakobov, was killed in the town in late November.
The attack came during a meeting in Sderot between Foreign Minister Tzipi Livni and Javier Solana, the European Union foreign policy chief. They were not harmed. (For more on Solana's visit, click here)
In a joint press conference with Solana, Livni rejected any possibility of a cease-fire with Hamas. "A cease-fire is a kind of deception," she said. "Even during periods of so-called quiet, Hamas takes advantage of the situation to smuggle arms."
During the press conference, Livni received a note from Sderot Mayor Eli Moyal, informing her of the woman's death.
"Qassams are the result of Hamas' strengthening, and this is a strategic problem that must be dealt with and we will keep fighting Hamas," she continued. "Fighting terror does not mean making deals with terrorist organizations, we must demonstrate a fundamental change in the field."
"No nation would tolerate the consistent rocketing of its citizens, and neither will Israel," David Baker, an official in the Prime Minister's Office, told Haaretz following the attack. "We will continue to take whatever steps are necessary to bring these attacks to an end and to prevent terror from being inflicted upon the residents of Sderot and the western Negev."
Saeb Erekat, an aide to Palestinian Authority Chairman Mahmoud Abbas, said Abbas is making efforts to restore the cease-fire that greatly reduced Israel-Palestinian violence in Gaza from November until last week.
Erekat told The Associated Press that Abbas is calling on international mediators to press Israel to halt its strikes and on Hamas to stop the rocket salvos.
Following the attack, hundreds of Sderot residents gathered around the town hall, throwing stones and breaking its doors. The protesters chanted "Arcadi for prime minister," in reference to billionaire Arcadi Gaydamak, who on several occasions has provided hundreds of Sderot residents with hotel stays in Israeli cities in order to give them a break from the rocket fire.
Earlier, the protestors also tried to block Livni from leaving the town.
According to the IDF, a total of 15 rockets were fired at the area on Monday. Two struck early in the day, one of which slammed into and damaged a road. No injuries were reported. Another rocket hit the area Monday evening, causing no injuries, and a rocket hit a field near Sderot later in the day, causing a fire but no injuries.
Some 15 rockets hit the Sderot area on Sunday.
Meanwhile Monday, the Israel Defense Forces Home Front Command distributed instructions on what to do in the case of a rocket attack to the residents of Netivot, which is located roughly 15 kilometers from the Gaza Strip and is in range of improved Qassams as well as Katyusha rockets.
Roughly one year ago rockets hit slightly to the west of the town, and the IDF is preparing for the possibility that further escalation in the Gaza Strip will bring rocket fire on Netivot and Ashkelon as well.
The IDF on Monday also called up 35 reserve medics on emergency orders to serve in Sderot, Ashkelon, and other parts of the western Negev, Army Radio reported.
The escalation in the Gaza Strip has spurred concern in the IDF that Hamas will again attempt to kidnap Israeli troops, Army Radio reported Monday.
Last June, Hamas and other armed groups attacked an IDF post on Israeli soil bordering Gaza, killing two soldiers and wounding four, one of whom, Corporal Gilad Shalit, was taken captive.
"Israeli forces in the area of the Gaza Strip have been instructed to raise their alertness level for fear that terror organizations may attempt to carry out kidnappings," the radio reported.
It said the concerns were increased after overnight Israeli air strikes, one of which hit the house of Hamas parliamentarian Khalil al-Haya in Gaza. The lawmaker was slightly injured in the attack, but eight others including seven members of his family were killed, and 13 people were wounded.