A senior Home Ministry official said an investigation has been ordered into the activities of IRF, which was registered under the Foreign Contribution Regulation Act (FCRA).
Mumbai-based Naik has come under the scanner after it was reported that his speeches have inspired some of the Dhaka cafe attackers. Maharashtra government yesterday ordered a probe into the speeches by the Muslim televangelist.
All such activities are contrary to the FCRA provisions and any violation invites punitive action.
IRF's source of foreign funding will also be examined thoroughly by the Home Ministry, the official said.
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An online petition has been filed with the Home Ministry listing all the allegations against IRF as well as its chief Zakir Naik.
Officials said according to an intelligence report the content of the "Peace TV", in which Naik regularly appears and gives sermons, is "not conducive" to the security environment in the country and poses "security hazard".
Naik, however, had released a statement, saying he "totally disagreed" that he inspired the act of killing innocent people in Dhaka. "There is not a single talk of mine where I encouraged one to kill another, whether Muslim or non-Muslim," he said.
New Information and Broadcasting Minister, M Venkaiah Naidu, had called Naik's speeches, as being reported in the media, as highly objectionable.
Naik's speeches are believed to have inspired some of the Bangladeshi militants, who killed 22 people, mostly foreigners, at an upscale restaurant in Dhaka last Friday.