A Palestinian attacker is also believed to have died in the attack on a main road near Bnei Brak, a suburb of Tel Aviv.
The attack follows an Israeli army incursion into the Rafah refugee camp in the southern Gaza Strip in which four Palestinians were killed and 17 injured.
In the West Bank, Israeli soldiers raided Palestinian towns and villages overnight, arresting more than 70 people.
Twelve people were injured in the attack near Tel Aviv.
The explosion happened during the morning rush hour.
Struggle with attacker
Reports say that a man approached a bus as it was at a stop. He tripped and fell as he was trying to get on.
The bus driver, Baruch Newman, has told the BBC that he and a passenger went to see if the man was okay.
He then saw explosives wires strapped to the man's body, so he pinned the man down and shouted out to the passengers on the bus to stay clear.
The man began to struggle, so Mr Newman decided to get up and get clear himself.
The attacker then got up, went to a bus stop and detonated his explosives.
BBC Jerusalem correspondent Barbara Plett says the attacks might have killed many more people had the bomber made it onto the bus.
There has been no claim of responsibility for the attack.
An Israeli Government spokesman, David Baker, said: "Palestinian terrorists have declared open season on Israelis."
The suicide attack is the first since back-to-back attacks on 18 and 19 September.
Israel responded to these attacks with a controversial 10-day siege of Yasser Arafat's headquarters in Ramallah.
Tanks and gunships
The latest Israeli army incursion into the Rafah refugee camp in the Gaza Strip started on Wednesday and continues into Thursday.
Two Palestinians - one a 12-year-old child - were shot dead by Israeli tank fire early on Thursday, Palestinian hospital sources said.
On Wednesday, at the start of the raid on Rafah, Israeli troops shot dead two Palestinian youths and wounded up to 17 others.
Palestinian witnesses said more than 20 Israeli tanks, backed by attack helicopters, moved into the camp from two directions, firing their machine guns.
The Israeli army says its soldiers were shot at and one was lightly injured when a tank went over some kind of explosive device.
The latest violence follows a major Israeli incursion into the Gaza Strip on Monday which left 16 Palestinians dead in Khan Younis - for which Israel was widely criticised.
The south of the strip has seen fierce fighting since Monday's incursion.
Settlements dismantled
On Thursday, the Israeli army dismantled two more Jewish settlement outposts in the West Bank.
Israeli army radio reported that soldiers evacuated a building near the Har Braha settlement outside Nablus that was occupied by three settlers.
The other outpost, near Ramallah, was uninhabited.
Two other outposts were dismantled by the army earlier in the week.
Jewish settlements in the West Bank and Gaza are considered illegal under international law.
Israel considers only the outposts not authorised by the government to be illegal.