Video shared on Sunday from the Orbit Festival in the north-eastern town of Nabeul sparked outrage on social media sites.
The governor of Nabeul, Mnaouar Ouertani, said that the club would "remain closed" until further notice.
An investigation has begun into the incident.
The footage shows clubbers at a party on Friday dancing to music played by two European DJs near the popular seaside resort of Hammamet.
The music included a dance version of the call to prayer, the religious act that Muslims perform five times a day.