Aljazeera said the woman was Zainab Abu Salim, 21, from the Askar refugee camp in Nablus.
Police said it was the first such attack in the city in seven months.
The blast tore through the French Hill district in East Jerusalem, which was captured by Israel in 1967 and annexed in a move not recognised internationally.
Witnesses said the woman blew herself up as she approached a security position near a hitch-hiking post mostly used by soldiers. Two border police were killed.
"She threw her head back and then there was an explosion," one witness, Debbie Segal, told Army Radio. "A few seconds later, her body burst into flames."
Segal said she was on her way home from work at a nearby hospital at the time of the attack.
"I stood five minutes at the hitch-hiking post. I noticed a pretty young Arab woman covered in a veil coming... to the hitch-hiking post.
"The border policeman was in a security post nearby. He called her and she came to him and made a head gesture making believe she didn't understand him. He continued talking to her and she answered him."
The woman then blew herself up.
It is thought that Israali soldiers
were targeted in the attack
Ambulances rushed to the scene and police quickly cordoned off the area, which was littered with broken glass and debris.
The al-Aqsa Martyrs Brigades, an armed group in President Yasir Arafat's Fatah movement, claimed responsiblity for the bombing.
It said it was avenging Israel's recent killing of several of its members in the West Bank cities of Nablus and Jenin.
The Palestinian Authority swiftly condemned the bombing, saying it opposed all attacks against civilians.
It condemns "all acts targeting Palestinian and Israeli civilians", Palestinian negotiations minister Saeb Uraiqat said.
"An end to the violence can only take place with the end of the Israeli occupation of Palestinian lands," he added.
The al-Aqsa Martyrs Brigades
Uraiqat called for US President George Bush and the Middle East diplomatic quartet of the United States, European Union, Russia and the United Nations to implement its international roadmap for peace.
Meanwhile, Israeli Prime Minister Ariel Sharon vowed that Israel would strike Palestinian fighters with "all force".
"In many cases we prevent heavy disasters. Sometimes things happen like what happened today. But we intend to continue our struggle against terror with all force," Sharon said on Israeli television.
Shock and grief
Anticipating an Israeli raid, hundreds of residents of the Askar refugee camp have rushed to Abu Salim's home to help her family remove furniture.
Israel routinely demolishes homes of Palestinian human bombers.
"I don't know what's happening," said her 12-year-old brother Tariq. "I don't know where she is. She isn't home".
Her father, Ali, recovering from surgery to open clogged arteries, collapsed and was taken to hospital after learning of his daughter's death.
Abu Salim's mother also fainted and was rushed to a local hospital.
Relatives remembered Abu Salim as a brown-eyed girl with a warm smile who had just passed high school graduation exams and had spoken of entering university.
The attack on Wednesday was the first of its kind in Jerusalem since 22 February when a bomber killed eight people on a bus.
Violence has surged in recent months since Israeli Prime Minister Ariel Sharon introduced his plan to evacuate Jewish settlers from the Gaza Strip and four of 120 in the West Bank by the end of 2005.
Israeli PM Sharon has treated
intifada with an iron fist
Analysts say Palestinian resistance fighters want to claim victory in any Israeli pullout, but the army is determined to smash armed factions before leaving.
This was at least the third attack in French Hill since the start of the latest Palestinian uprising against Israeli occupation in September 2000.
Israel sees French Hill as a neighbourhood of Jerusalem but it is widely viewed internationally as an illegal settlement built on occupied land.