Videos and photos shared widely on Facebook and Twitter showed the women purportedly following the lead of a woman who was arrested for a similar demonstration last month.
The as-yet unidentified woman was detained in Tehran after standing on a telecoms box, taking off her headscarf and holding it in the air on a stick.
The 31-year-old protester known as the "Girl of Enghelab Street", later identified as Vida Movahed, took off her headscarf on a street in the capital Tehran.
Movahed's identity was initially a mystery until Iran's most prominent human rights lawyer, Nasrin Sotoudeh, established she had been arrested.
Public concern mounted for Movahedi's safety after reports of her arrest, particularly with the authorities clamping down on protests and possible dissenters as antiestablishment unrest spread to dozens of Iranian cities in late December and early January.
Several detainees have died in custody.
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While the tariff is 30 percent this year, it'll decrease by five percent each year, eventually reaching 15 percent in year four. Tariffs for the latter will be raised to 20 percent on 1.2 million units in the first year and then 50 percent after that.
Around 300 people remain imprisoned as sporadic protests continue across the country, according to Iran's interior ministry.
Just a few months after the establishment of the Islamic Republic in 1979, a law forcing women to not only cover their heads, but also wear loose clothing to hide their figures, came into effect despite mass protest.
On Monday, reacting to the new protest, Sotoudeh wrote: "Today, I was informed that a second woman has stood on a telecoms box in the same place, holding up her hijab aloft on a stick".
"This should be seen as part of a larger struggle of Iranian women for equality and to have control over their own bodies, and can even be traced back to women's resistance of forced unveiling during the reign of Reza Shah", said Sussan Tahmasebi, an Iranian women's rights activist.
Women who violate the country's dress code will be sent to classes on Islamic values instead of being arrested.
People from all over the world, are supporting the Iranian women and think that the veil law should be banned and women should be treated equally as men.