The three, all Indian Muslims, were arrested on suspicion of being involved in the attacks on commuter trains and stations in India's financial hub on July 11, a police official said.
"Yesterday, on July 20, we arrested three suspected accused in connection with the bomb blast case," KP Raghuvanshi, chief of Mumbai's anti-terrorism squad, told a news conference.
Two of them were picked up from the Madhubani district of eastern Bihar state, Raghuvanshi said, but he gave no details of the arrest of the third. However, local TV said the third man was arrested in Mumbai.
Asked which organisations these men belonged to, Raghuvanshi said their links appeared to come from Nepal and Bangladesh, but he said they were also in some way connected to Pakistan. He gave no explanation.
India has said in the past Pakistan-based groups have set up bases in Bangladesh and recently two Pakistani men were detained in Nepal, although their links with the Mumbai blasts were denied.
Islamabad has denied any connection with the bombings and on Thursday Pervez Musharraf, the president, said New Delhi should desist from a "blame game".
Raghuvanshi said 0.5kg of black powder recovered from the house of one of the arrested men was being tested.
The men were produced before a court and sent to police custody for 10 days at the request of the public prosecutor.
"On the basis of interrogations so far, we have learnt that these people are linked to terrorist activities," Raghuvanshi said. "On their role in the bomb blasts, we will tell you after the interrogations."
More arrests were likely, he said.