The militant Islamic group, Hamas, says it carried out the attack.
The explosion happened near the city's main synagogue on Allenby Street - one of Tel Aviv's busiest shopping districts - just after 1300 local time (1000 GMT).
Palestinians say that, in response, Israeli tanks have opened fire on the headquarters of Palestinian leader Yasser Arafat in the city of Ramallah.
It is the second bomb attack in two days. Another group, Islamic Jihad, says it carried out a suicide bombing on Wednesday which killed an Israeli policeman in the north of the country.
These are the first fatal suicide attacks in Israel for six weeks, although violence has continued in the West Bank and Gaza Strip.
Revenge
Hamas sent a fax to the AFP news agency saying Thursday's attack was its latest act of retaliation for the killing of its leader, Sheikh Salah Shahada.
He died in a missile attack in July in which at least 15 people were killed, including several children.
"At 12:55 this afternoon, a martyr from the Ezzedine al-Qassam Brigades took bus number 4 and blew himself up amid the Zionist passengers," the Hamas fax said.
Hours later Israeli tanks entered Yasser Arafat's Ramallah compound, opening fire.
"Tanks and jeeps are inside the compound and surrounding our office from all sides. There is fierce shooting. Two of our men have been injured but the president is fine," one of Mr Arafat's bodyguards told Reuters news agency by phone.
The army move came as Israeli Prime Minister Ariel Sharon called an emergency cabinet meeting and curfews were reported to have been reimposed on a number of West Bank cities.
Earlier on Thursday, a 10-year-old Palestinian child was killed by Israeli tank fire in the West Bank town of Ramallah.
The boy was shot in the chest after he went outside to buy cigarettes for his father, his mother said.
Packed
More than 40 people were injured in the Tel Aviv blast - several of them are in a serious condition. They include two British students, one of whom is described as 'critical'.
Police say the suspected suicide bomber was at the front of the packed bus when the device went off.
Ambulances raced through the busy lunch-hour traffic, and emergency workers wheeled blood-spattered casualties between vehicles.
An eyewitness, identified only as Sarit, told Army Radio: "We heard an explosion, very big. We saw a large cloud of smoke and immediately lots of police came.
"People came out to help with first aid. We're trying to give them water. We saw the front of the bus and it apparently caught on fire."
The Palestinian leadership responded by condemning all attacks on civilians. Senior negotiator Saeb Erekat said that in the six -week period in which there had been no suicide attacks, the Israeli army had killed 71 civilians, including the child killed on Thursday.
Observers say the attack is a setback for Palestinian leader Yasser Arafat and his Fatah faction which has been arguing that attacks within Israel, which many see as counter-productive, should stop.
Israel has accused Palestinian security forces of "not lifting a finger" to stop such attacks.
The BBC's Barbara Plett, in Jerusalem, says the recent Israeli occupation of the West Bank, tight curfews and arrests of militants have enraged the Palestinians. Both the Islamic Jihad and Hamas have threatened a resumption of attacks on Israeli targets.
Israeli is demanding a total cessation of violence before any start to a fresh peace plan proposed by international leaders.