Witnesses said the entire rear portion of the bus was torn apart and another bus and a motorcycle were also hit by the force of the blast.
Indian police immediately blamed the attack on an Islamic group, although no-one has claimed responsibility.
"From whatever information we have, the blast was loud and a big one," a police official said.
Witnesses described scenes of panic as the bomb detonated, shaking nearby buildings and rattling windows.
Sanjay Nirmal, a Mumbai resident, said the blast was so loud that a woman holding a baby lost her grip and dropped it on the ground.
Eyewitness Kishore Vaghela added: "The blast was so big that it was heard two to three kilometres (more than a mile) away. I ran to the spot and saw what happened and helped carry the victims to the hospital."
"The blast was so big that it was heard two to three kilometres (more than a mile) away. I ran to the spot and saw what happened and helped carry the victims to the hospital"
As police and forensic experts combed the area around the bus wreckage, Bombay Police Commissioner R.S. Sharma pointed the finger at the Lashker-e-Taiba group.
Islamic group blamed
Lashker is one of the two groups that New Delhi blames for the December 2001 attack on its parliament which left 15 people dead.
The organisation is fighting to remove Indian forces from the Muslim-majority state of Kashmir.
Police said in recent days they have received information that groups were planning to launch an attack either in New Delhi or Mumbai.
Krispashankar Singh, home minister of Maharastra state, said the explosion could be linked to earlier deadly attacks on public places in the city.
And police commissioner Sharma said there were parallels between Monday's blast and an attack in December 2002, when two people were killed and 27 injured by another Mumbai bus bomb.
In January this year, 30 people were wounded when a crude bomb planted in a bicycle exploded in a crowded street in a Mumbai suburb.
And in March a bomb planted on a suburban train killed 11 people.
Mumbai was also hit by a series of bomb blasts in March 1993 which killed more than 250 people and which were allegedly orchestrated by the city's criminal underworld.