Tamil Nadu's Chief Minister Jayalalithaa Jayaram said her government was forced to impose the 15-day ban to prevent unrest across the state, because there was "every apprehension" that protests outside cinemas would turn violent.
"When you know that there's going to be violence in a certain situation, in a certain place, it's the duty of the government to do whatever is possible to prevent that happening," the former actress told reporters in Chennai.
She said the state did not have enough police to maintain law and order outside more than 500 cinemas that were due to show the movie.
Haasan, who is due in Mumbai on Friday for the film's release there, has reportedly agreed to modify his movie to appease the protesting groups.
"If the leaders of the Muslim organisations and Mr Kamal Haasan can sit together and work out an amicable agreement, the government of Tamil Nadu will do everything possible to facilitate that," Jayaram said.
The ban comes in the same week that British author Salman Rushdie also faced the wrath of Muslim groups, forcing him to cancel a trip to the eastern city of Kolkata to promote the film "Midnight's Children".
Rushdie, whose novel "The Satanic Verses" is seen as blasphemous by some Muslims, was also forced out of India's biggest literature festival last year after apparent threats to his life.
The latest controversies have sparked a fresh round of concern over free speech in India.
Author Manu Joseph wrote on Thursday that the country "is a paradise for those who take offence because the first reaction of the state is to appease those who claim to have been offended".
An editorial in the Mid Day tabloid, decrying a "herd mentality", said that "more and more people are joining in to stifle any kind of expression perceived as offensive" without even seeing the film or reading the book in question.
Indian film stars have rallied around Haasan since the ban on his film, which has already passed the country's censorship board.
"Go stand outside the cinema hall (and) insist on seeing the film," Bollywood megastar Salman Khan told his huge following on Twitter on Thursday.
Another leading actor, Shah Rukh Khan, said it was "the most unfortunate thing to happen to a film".
India's Information and Broadcasting Minister Manish Tiwari told NDTV that each case was different, but state governments "need to lean in favour of freedom of speech and expression" even amid law and order fears.
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