Prophet Mohammed’s grandson, Hussein, was killed in 680 AD and there is a national day of mourning in Iraq every year.
The night, known as ‘Ashura’, is meant to be a quiet day of sadness.
However, citizens were angered after the Dijlah television centre broadcasted a show that included singing and dancing.
The channel, owned by Iraqi businessman and politician Jamal Al Karabouli, aired the programme which drew thousands of people to the TV station in Baghdad.
Marching and demanding blood were armed hordes of Shiite Muslims who surrounded the station and then stormed it.
Images show fires being started and local reports said the fire spread to a neighbouring residential building but protesters prevented fire crews from putting it out.
Security forces accompanied protesters but did not try to stop them, the report said.
An arrest warrant was issued for Mr Karabouli on Monday for violating the Iraqi Penal Code’s religious offences.
Mr Karabouli is likely to be handed a detention sentencing that will not exceed three years or pay a fine.
Dijlah staff quit the TV station in protest also.
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