They were identified as Mikhail Khan, Rabiul Islam and Naziur Rahman. All of them are from Gopalganj district.
Police said the three were staying in Kolkata for a few months on pretext of medical treatment of a relative.
"But they were actually raising funds and trying to recruit local Muslims for militant activity," said an officer of Kolkata police special task force.
Bangladesh intelligence has confirmed the identity and affiliations of the three arrested.
An intelligence official in Dhaka told that the three would surely have links with other JMB activists active in West Bengal and south India. "So it was necessary to launch follow-up operations based on leads these three may provide."
Bangladesh has long expressed worries about their Islamist terrorists escaping into India, especially into West Bengal, some of whom return to the country to launch attacks.
Indian and Bangladesh have developed close intelligence cooperation in the last decade as part of prime minsiter Sheikh Hasina's determined bid to stamp out terror and not allow its soil to be used for terror strikes.
Some top JMB leaders like Abu Musa have been arrested in West Bengal, but few like Salahuddin Salehin are still at large.