Hussein Zain, president of the association, deplored the move that has insulted the position of the radio station and those who listen to it, RT Arabic reported.
He added that the association will pursue the matter to make sure that the individual is tried and punished for his offensive action.
Mohammad Ashraf, a young Egyptian comedian, recently shared a video in social media in which he mocks the Quran radio.
This has drawn criticism from many social media users who have called for his trial.