Police said many of those hurt were caught by flying glass, and witnesses spoke of seeing bodies in the street and shop windows blown out by the force of the explosion.
If confirmed, it would be the first suicide bombing carried out by a woman in Israel during 16 months of violence. Police are unsure if the woman meant to kill herself or if the bomb exploded prematurely.
The attack, the third on an Israeli city centre in a week, is likely to trigger fresh Israeli retaliation and add to mounting pressure on Palestinian leader Yasser Arafat to do more to clamp down on militants.
Egypt and Jordan both condemned the bombing, but say Israel bears a responsibility for the continuing violence.
They are the only two Arab states with peace treaties with Israel, and the BBC's Caroline Hawley in Amman says they have watched the escalating crisis across their border with growing concern.
Arafat blamed
Police spokesman Gil Kleiman said there was "a host of possibilities" as to how the bomb went off on the junction of Jaffa Street and King George Street.
"We are not calling her a suicide bomber, just a bomber. She is not an innocent bystander," he said, adding she was believed to be Palestinian.
The Palestinian leadership strongly condemned the attack.
But Raanan Gissin, a spokesman for Israeli Prime Minister Ariel Sharon, said: "Arafat is responsible since he encourages terrorists to commit suicide acts."
The bomber has been linked to the towns of Bethlehem and Nablus and Palestinian security sources say they have evacuated buildings in both places, including prisons, because of fears of an Israeli reprisal.
They say that the prisoners, some from militant groups, are being kept under watch.
The Palestinians have repeated their calls for the US to send peace envoy Anthony Zinni back to the region to oversee peace efforts.
But Vice President Dick Cheney kept up US pressure on Mr Arafat.
He told a Sunday TV show he found it "hard to believe" the Palestinian leader was not involved in a recent arms smuggling incident, when a freighter carrying 50 tonnes of arms was intercepted by Israel, which said the weapons were for the Palestinian Authority.
"The people that were involved were so close to him [Arafat] it's hard to believe that he wasn't involved," Mr Cheney said.
Shop destroyed
Jerusalem's latest attack occurred next to a shoe shop near the Sbarro pizzeria where 15 people were killed by a Hamas suicide bomber on 9 August 2001.
Last week a Palestinian gunman went on a shooting spree
on Jaffa Street, killing two women and injuring more than a
dozen people before he was shot dead by police.
According to an AFP reporter on the scene of the latest blast, body parts of the woman bomber were scattered in front of the Freimann and Bein shoe shop.
The force of the explosion destroyed the shop's interior. An 81-year-old Israeli man was killed.
An emergency services official said two people were seriously wounded.
Correspondents say that with Israeli security tighter than ever, the group that carried out this attack may have believed that a woman was more likely to pass unnoticed, or unsearched, through the many checkpoints and road blocks.