A row had erupted after the national award-winning lyricist had reportedly made the comments against Andal, a Hindu Goddess, at a function in Rajapalayam.
Police said a case was registered against Vairamuthu, 64, based on a complaint from a Hindu Munnani functionary.
The complainant, Suri, stated that devotees of Goddess Andal were hurt by the poet's remarks.
They threatened to go on an indefinite fast if he did not do so by January 16.
Investigation is underway, police said.