A police spokesman, inspector S Goshal, said the majority of the detentions were made overnight on Thursday in Malwani, a northeastern suburb of the city.
He said that none of them has been formally arrested or charged and that they were detained only for questioning to help with the investigations into Tuesday's co-ordinated bombings.
A N Roy, a police commissioner, said those arrested include known thugs, gangsters and troublemakers who might have information about the culprits.
The arrests came a day after the police chief of Maharashtra state, of which Mumbai is the capital, said investigators were looking into a possible link with Lashkar-e-Tayyaba, one of the several Kashmiri militant groups fighting for independence.
Also on Thursday the Indian prime minister, Manmohan Singh, and his government said they were committed to wiping out terrorism.
A cabinet statement said: "Nothing will deter us from our firm policy to fight this menace till it is wiped out. We are determined to apprehend and bring to justice all those responsible for the evil acts in Mumbai."
Singh was to visit Bombay on Friday for an assessment of the investigations into the bomb blasts.
Business as usual
Meanwhile, Mumbai’s commuters were back jamming onto trains as usual on Thursday.
Trains were crowded as normal on
In a city of 16 million, Mumbai's suburban railway is crowded around the clock, with each nine-car train often carrying three times the official 5,000 passenger capacity during peak hours.
Some people stayed away from work the day after the blasts, but the trains were busy on Thursday, although with a sense of unease as many checked under their seats and kept an eye on luggage.
Mumbai's authorities are considering installing metal detectors and closed circuit television at all railway stations.