"Exclusion powers are very serious and no decision is taken lightly or as a method of stopping open debate on issues."
This is the first person who has been excluded from the UK since Ms May became home secretary last month.
Mr Naik is based in Mumbai (Bombay) where he works for the Peace TV channel.
He was due to address events at Sheffield Arena on 25 June and Wembley Arena on 26 June.
The BBC's Sanjiv Buttoo says that he is recognised as an authority on Islam but also has a reputation for making disparaging remarks about other religions.
Peace TV itself describes him as "a medical doctor by professional training… and a dynamic international orator on Islam and comparative religion".
"Dr Naik clarifies Islamic viewpoints and clears misconceptions about Islam using the Koran," the channel's website says.
A spokesman for Mr Naik said it was "deeply regrettable" the UK government had "bowed to pressure" from certain groups to exclude him.
He said Mr Naik had been holding talks in the UK for 15 years and the decision to bar his entry was disappointing.
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