The attack at the Hasharon mall, the target of a similar bombing less than six months ago, was roundly condemned by Israel, the Palestinian Authority and the US, which said it would only undermine the peace process.
Responsibility was claimed by Islamic Jihad, the group behind all suicide bombings since the armed factions signed a truce in March.
Israeli Defence Minister Shaul Mofaz gave the green light for the army to resume targeted killings of Islamic Jihad activists after the attack.
Israel retaliates
Israel also sealed off the West Bank and Gaza Strip, barring entry to the Jewish state and annexed east Jerusalem, and Mofaz ordered the army to "regain control" of Islamic Jihad strongholds in the West Bank.
The website of the Haaretz newspaper said the army was preparing a "vast operation" in northern Gaza in retaliation for the suicide bombing.
Police said the bomber was carrying several kilograms of explosives in a bag but was prevented from entering the mall by a policeman and a guard at around 11:30 am local time (0930 GMT).
Apart from the bomber, four people died at the scene and a fifth died in hospital where another 25 were receiving treatment.
An Agence France Presse correspondent said four badly burned bodies could be seen lying on the road outside the mall.
Glass and rubble littered the area while nearby buildings had their windows blown out.
Greater carnage was prevented by a policewoman who spotted the bomber and alerted guards.
They grabbed the bomber but he somehow managed to detonate the explosives.
"I shouted for them to get his hand out of the bag, so the guard grabbed him, but he pressed something, I was looking into his eyes as he pressed something and blew up," said the policewoman, Shoshi Atiya.
Second attack
Five people were killed outside the same mall on July 12 in an attack also carried out by Islamic Jihad.
Monday's blast was the first suicide attack since a bombing in the northern town of Hadera in late October.
Islamic Jihad named the bomber as Lotfi Amine Abu Saada, 21, from a village near Jenin in the northern West Bank.
Palestinian leader Mahmud Abbas condemned the attack as an act of "terrorism", ordering the security services "to catch whoever is responsible for this attack and bring them to justice."
But Mr Mofaz said the bloodshed demonstrated the Palestinian Authority's (PA's) inaction.
"The weakness that the PA is showing time and time again in dealing with Islamic Jihad is testimony to the fact that they have no intention of dealing in a real and substantive way with the terror infrastructure," he told Israeli army radio.
Mr Mofaz also said he was seeking legal approval to resume the controversial policy of demolishing the family homes of suicide bombers.
Armed clashes broke out in the town of Jenin between Palestinian security forces and followers of Islamic Jihad "celebrating" the bomb attack. There were no reports of casualties in the clashes.
Bomber illiterate
The bomber's father said he had not known of his son's links to Islamic Jihad and only found out what had happened when hordes of people gathered at his home.
"My son left school at the age of 11 and was virtually illiterate," Amin
Abu Saada said. "He would do his prayers but he was not very religious."
Egypt, which helped broker March's truce, said the bombing was counterproductive.
Such attacks "greatly harm the chances of the Palestinians to achieve their rights and establish their own state", Foreign Minister Ahmed Abul Gheit said.
Jacob Walles, US consul general for east Jerusalem, said the attack was carried out by "enemies of peace" who were undermining the Palestinian Authority.
EU foreign policy chief Javier Solana agreed it was "clearly destined to undermine the recent positive and concrete steps taken by the Israelis and Palestinians with a view to re-establishing confidence between the two parties."