The clip shows three men and three unveiled women singing and dancing to the tune in the streets and on Tehran rooftops.
"After a vulgar clip which hurt public chastity was released in cyberspace, police decided to identify those involved in making that clip," Tehran police chief Hossein Sajedinia was quoted as saying by the ISNA news agency.
"Following a series of intelligence and police operations and after coordinating with the judiciary, all the suspects were identified and arrested."
Conservatives say many young Iranians are abandoning Islamic values and turning to a more Western way of life.
Under Islamic law, in force in Iran since the 1979 revolution, women must cover themselves from head to toe.
More than a decade ago a "morality police" unit was formed to verify that women scrupulously respect the dress code in public.
The Internet is also heavily filtered in Iran, with the authorities blocking access to popular social networking sites.
Civil liberties and women's rights have returned to the forefront since President Hassan Rohani's election last June.
But Conservatives regularly denounce what they see as laxity on the part of the authorities on women covering up or on behaviour deemed offensive to Islam.
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