A video, widely shared online since Sunday, shows clubbers dancing at the weekend to music that includes the call to prayer at the club in the northeastern town of Nabeul.
The footage sparked a storm of debate on social media.
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The party, near the popular resort of Hammamet, had been organised by two European DJs.
"After confirming the facts, we decided to close this nightclub" until further notice, Nabeul governor Mnaouar Ouertani said.
He said an investigation had been opened and the club's manager detained "for violation against good morals and public outrage against modesty".
"We will not allow attacks against religious feelings and the sacred," Ouertani added.
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