It registered a case against Mr Azharuddin and the others on 30 May, according to a press statement
The Sri Lanka bombings killed more than 250 people and wounded 500 others.
Five other men have been detained for questioning, said India’s National Investigative Agency (NIA), which conducted the raids and made the arrest.
It registered a case against Mr Azharuddin and the others on 30 May, according to a press statement. State intelligence and local police are now conducting further raids in Ukkadam, a neighbourhood in Coimbatore, where officials say three of the suspects, including Mr Azharuddin, live.
Federal investigators accuse all six suspects of “propagating” IS ideology and attempting to recruit “vulnerable youth” to carry out attacks in southern India, including Tamil Nadu, the state where Coimbatore is located.