The Al-Sharq daily said the Muslim migrant, whose nationality was not stated, works as a barber in the Gulf state.
He was arrested after a man reported him to police for allegedly harassing his maid by plying her with visiting cards with his phone number on them.
Police raided the barber's shop to question him over the claims but found him drunk on the premises.
Non-Muslims may drink alcohol, which is banned in Qatar other than in hotels, but they require a special permit to do so.
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