A bench comprising Chief Justice Dipak Misra and Justices A M Khanwilkar and DY Chandrachud also extended relief to the director of the Malayalam movie "Oru Addar Love", who had also been named in the complaints.
The song "Manikya Malaraya Poovi" has run into controversy and the Hyderabad police filed a case against the actor last week following a complaint from a group of young men. The men said the song has a reference to the wife of Prophet Muhammad, which they find objectionable. A Hyderabad-based Islamic seminary issued fatwa against the song and demanded that it be removed from the film. Another case was filed subsequently in Maharashtra.
The police cases accused the actor and the director of deliberate and malicious acts intended to outrage religious feelings.
Admitting that they have been "baffled" by the complaints, Mr Beeran said it was likely that the people in Hyderabad read an English version and the song's meaning might have been literally "lost in the translation".
Ms Varrier shot to fame earlier this month with a wink and a smile after a promotional video clip from the film won hearts on social media.