The action was taken after the home ministry found that Naik's NGO Islamic Research Foundation's FCRA licence was renewed recently despite several ongoing probes, including one by it.
The IRF was banned for five years by the government last year under the UAPA for its alleged terror activities.
Naik is said to have acquired citizenship of Saudi Arabia but this has not been confirmed yet.
The NIA has questioned around 20 associates of Naik, including his sister Nailah Naushad Noorani, in connection with its investigation, they said.
The NIA has asked him to him to appear before it on March 30 in a case filed against him under an anti-terror law.
Home Minister also said CDs of Naik's speeches are being examined and asserted that the government will not compromise on the issue of terrorism.
The home ministry also ordered a probe by the Computer Emergency Response Team-India to ascertain whether there was hacking of government software systems as there have been several instances where licences of NGOs under scrutiny were renewed automatically.
Controversial Islamic preacher Zakir Naik on Sunday claimed that there has been no misuse of funds by his banned NGO and rejected all allegations of involvement in terror-related activities.