Two of the suspects were living in the area for three months without a rent agreement.
Four Bangladeshi terrorists have been arrested from two places in Bhopal, Madhya Pradesh Home Minister Narottam Mishra said on Sunday.
They belong to the Jamaat-ul-Mujahideen Bangladesh (JMB), the terrorist group involved in the 2018 Bodh Gaya bombing, he said.
Those arrested have been identified as Fazhar Ali alias Mehmood, 32, Mohammad Aqeel alias Ahmed, 24, Zahooruddin alias Ibrahim, 28, and Fazhar Zainul Abdeen alias Akram Al Hasan, anti-terrorism officials said.
According to them, laptops, religious literature and explosive substance have been seized from both the places, which were being used as hideouts.
The operation was carried out by the anti-terrorism squad and central intelligence agencies.
The local police station, just metres away from one of the houses, was not informed, sources said.
The arrests were made from two houses in Karond and Aishbagh areas between Saturday night and early Sunday.
Two of those arrested from the Aishbagh area were identified as Ahmad and Mufti Sahab by locals.
They were living in a multi-storey building without a rent agreement or police verification for the last three months, sources said.
Around 60 police personnel arrived at the building at around 3 am, one of their neighbours said.
They fired a gun to unlock the door and sealed the house after the arrests, he said.