There is a shortage of power and water in Beit Hanoun
She died after detonating her bomb near Israeli soldiers in Beit Hanoun, focus of a six-day military offensive.
Earlier, a 17-year-old Palestinian boy was killed in an air strike on the northern town of Jabaliya.
Israel says it is targeting rocket-firing Palestinian militants operating from northern Gaza.
But Palestinian officials have accused Israel of carrying out a "massacre".
About 50 Palestinians have died in the country's latest military incursion into the area.
Curfew imposed
The Islamic Jihad militant group said the female suicide bomber was one of its members, the BBC's Alan Johnston in Gaza says.
A radio station linked to Hamas reported that many civilians were injured when the woman blew herself up, AP reports.
During the Jabaliya air strike, at least four people were hurt in the attack near a school, Palestinian officials told Reuters news agency.
I am following with deep worry the news about the grave deterioration of the situation in the Gaza Strip, and I want to express my closeness to the civilian population, which is suffering the consequences of the acts of violence
Pope Benedict
Gazans full of fear
The Israeli military said its aircraft had attacked a group of militants retrieving a device used to fire a missile, in Monday's attack.
But the Palestinians said the plane missed its target and, instead, struck close to a school.
The entire town of Beit Hanoun remains under Israeli control and troops have ordered residents to stay indoors.
Our correspondent says there are severe shortages of water and power, and the arrival of a small United Nations aid convoy on Monday sparked frantic scenes.
Israeli Prime Minister Ehud Olmert has declined to say when the operation centred on Beit Hanoun will end, but insists Israel has no intention of reoccupying the Gaza Strip.
Israeli forces have made regular incursions into Gaza and the West Bank since the capture of an Israeli soldier in a cross-border raid by Palestinian militants on 25 June.
Despite the crackdown, a rocket hit the Israeli border town of Sderot on Sunday, but no-one was hurt.
Palestinian Authority President Mahmoud Abbas and Prime Minister Ismail Haniya have called the operation a "massacre" and urged the UN Security Council to convene to discuss the issue.
International criticism
On Sunday, Pope Benedict XVI said he was very worried about the situation in Gaza, and called on all sides to work to stop the bloodshed and to immediately resume direct and concrete negotiations.
The Red Cross has criticised the killing by Israeli force of paramedics
The European Union presidency, currently held by Finland, has issued a statement deploring "the growing number of civilian casualties the Israeli military operation has caused".
The International Red Cross also criticised Israel for the killing of two medical workers, saying that the paramedics and their vehicle were clearly marked.
A Palestinian teenager was killed and seven others, including six children, injured in an Israeli airstrike near a school in the town of Beit Lahiya, according to Dr. Muawiya Hassanin, a local emergency services official. 

Israeli military officials said that the strike targeted militants who were retrieving a device used to fire missiles. 
 
Israel's incursions into northern Gaza, which are aimed at curbing rocket attacks by Palestinian militants, have killed over 50 people over the last six days.

Friday saw 17 killings, including the gunning down of two women outside a mosque in Beit Hanoun. At least seven people, including a 12-year-old girl were killed by Israeli action on Saturday, and three others yesterday. 

The Israeli Prime Minister Ehud Olmert denied that his country was planning to re-occupy Gaza, and said that the offensive is aimed at stopping rockets from being fired into Israel by Hamas militants.

Palestinian Authority President Mahmoud Abbas has termed the incidents "massacres" and has called for the UN Security Council to discuss the issue.

Israeli troops have regularly made incursions into Gaza following the capture of Gilad Shalit in June this year.