Islam allows intonation of Koranic verses, and recordings of chanting are frequently heard in marketplaces or on the radio and television, but singing them to musical accompaniment is prohibited.
Prosecutor Adnan Fakhro said authorities have "investigated the incident of a video published on social media of a student singing verses of the holy Koran, accompanied by musical instruments."
The report, which did not identify the instruments used, said the incident took place during an art competition.
The trio are being held pending further investigation.