The regime's "moral security plan", which bans women from wearing loose headscarves and exposing skin on their legs and bans men from displaying western-style haircuts and now necklaces, is enforced by thousands of special forces.
The ban on necklaces comes after a move to criminalise dog ownership as "a blind imitation of the vulgar culture of the west", the Guardian reports.
Under Islamic law dogs are considered unclean, but a few Iranians still keep dogs as pets.
Last year Ayatollah Makarem Shirazi, a prominent hardline cleric, issued a fatwa against keeping dogs.
The Irna state news agency said more than 70,000 trained forces, known as "moral police", had been sent to Teheran and other major cities to enforce the new rules.
"The enforcement of the moral security plan was requested by the nation and it will be continued until people's concerns are properly addressed," said Ahmadreza Radan, the deputy commander of the Iranian police.
The programme is supported by Ayatollah Ali Khamenei but last year president Mahmoud Ahmadinejad said that he did not approve of the crackdown.
