Another 50 people were injured in the blast, which occurred at The Mayor's Felafel restaurant, close to the central bus station in the crowded Neve Shaanan area on Monday afternoon.
Ehud Olmert, the acting Israeli prime minister, said Israel "would react in a necessary way" to the bombing.
Responsibility for the attack has been claimed by the Palestinian organisation, Islamic Jihad.
The group identified the bomber as Sami Salim Mohammed Hammed.
In a video released by the group and broadcast by the Arabic TV channel, Al-Arabiya, Hammed said the bombing was dedicated to the thousands of Palestinian prisoners in Israeli jails, adding: "There are many other bombers on the way."
The bombing was the first attack in Israel by Palestinian groups since January and came hours before the swearing-in of the new Israeli parliament.
Palestinian groups had vowed to take revenge after recent Israeli military strikes in northern Gaza that left 18 Palestinians dead.
It is the first suicide bombing since Islamist group Hamas formed a new government in the Palestinian territories more than two weeks ago.
A witness, Moussa al-Zidat, said a security guard outside the restaurant asked the suspected bomber to open his bag.
"This attack violates the Palestinian national consensus and runs contrary to our interests"
"I saw a young man starting to open his bag. The guard begins opening the bag, and then I heard a boom."
Live footage on Israeli television showed bystanders with blood on their shirts and the wounded being treated by the side of the road.
Car windscreens were shattered by the blast which blew out the windows of nearby buildings.
A witness, Israel Yaakov, said the blast killed a woman who had been standing near her husband and children, who were lightly wounded.
"The father was traumatised, he went into shock. He ran to the children to gather them up and the children were screaming, 'Mom! Mom!' and she wasn't answering, she was dead already ... it's a shocking scene."
Gideon Meir, an Israeli Foreign Ministry spokesman, said Israel held Hamas ultimately responsible for such attacks.
The wounded were treated by the
the side of the road
"From our point of view, it doesn't matter if it comes from al-Aqsa, Islamic Jihad or Hamas. They all come out of the same school of terrorism led by Hamas," he said.
It is the second time the same restaurant has been hit this year.
Fifteen people were injured at the fast-food outlet on January 19 in a bomb attack claimed by Islamic Jihad.
Meanwhile one Palestinian was killed and two wounded by an Israeli artillery shell in the northern Gaza Strip town of Bait Lahya according to medics.
The Israeli military has been firing towards areas where militants launch cross-border rocket attacks.