The Indian Prime Minister Manmohan Singh described the explosions as a “shameful act” and called on people to “remain calm and not to believe rumours.” He has called an emergency meeting.
Mumbai has seen bloody bombings in the past – with rival Hindu and Muslim extremists launching attacks.
There are suspicions that Islamist militants fighting Indian rule in Kashmir may have been involved this time.
Pakistan, which has been accused by India of aiding the militants in the past, has condemned the blasts.
Just a few hours earlier suspected Islamists killed seven people, six of them tourists, in a series of grenade attacks in Kashmir.
Mumbai, which used to be called Bombay, is a sprawling metropolis of 17 million people.