At least 29 people have been arrested for taking part in the protests so far, according to Iranian police, and dozens of videos have emerged from across Iran of women taking the same symbolic stand by climbing to a prominent spot and holding aloft a hijab.
The protest gained global attention on December 27 when Vida Mohaved, 37, a mother of one, stood on top of a telephone box on Enghelab Street in Tehran and hoisted a white hijab on a stick. When police pulled her down, her family turned to Sotoudeh.
The 54-year-old lawyer said she was impressed with the younger woman's defiance. "She stood there waving her scarf in the air and did not move or end her protest until the moment that she was arrested.
"She was determined to make a very important point. It was a very public show, and also it was peaceful. All civil rights movements around the world have succeeded when they have been based on these two elements. There is no reason as to why this one in Iran should not succeed too."
Sotoudeh passed the bar exam in 1995, but it took another eight years before she was finally given a permit to practise law. Since then she has represented defendants sentenced to die for crimes committed when they were children, opposition politicians and Shirin Ebadi, the Nobel Prize-winning Iranian dissident.
When Sotoudeh was arrested in 2010 and went on hunger strike, her case led to a widespread international outcry. The US said her conviction was part of a "systematic attempt" by Iran "to silence the defence of democracy and human rights".
She said she was not surprised to see young women like Mohaved protesting the hijab. "It has been happening in Iran for the last 40 years non-stop, but with ebbs and flows."
Ayatollah Khomeini, the founder of the Islamic republic, promised in early 1979 that the hijab would not be compulsory under his new government. But within weeks, he had gone back on his word and women were ordered to wear a headscarf outside the home.
On March 8, 1979 - International Women's Day - around 100,000 bareheaded Iranian women protested in Tehran against the new law. Their protest failed, but Sotoudeh said she saw the current protesters as the political daughters of those early resisters.
Holly Dagres, the curator of The Iranist newsletter, said Iranian women subverted the hijab law in small ways every day. "They constantly defy the rules by letting their headscarves inch back or fall off by 'accident', wearing hats in the streets and so on."
The new protests have been fuelled by social media and brought to the attention of the world by My Stealthy Freedom, a site that documents women's resistance to the hijab law.
"I wake up every day with the voices of these women in my inbox," said Masih Alinejad, the founder of the site. "I am full of hope. Civil disobedience is the first step to gain our victory."
Most of the protesters have been young liberal women, but in recent days others have joined. One video showed an elderly lady climbing on to an icy fountain and lifting her hijab with her walking stick. Some men have been arrested for solidarity protests. One of the most striking images is of a religious woman wearing a chador herself but demonstrating for the rights of others to choose not to do so.
The Iranian regime has so far struggled to respond to the protests, arresting some demonstrators but ignoring others and simultaneously denouncing the protests as an act of foreign subterfuge and dismissing them as "an emotional, childish act".
Sotoudeh said the ambivalent response reflected the contradictions of the Iranian system, where hardline clerics have supreme control, but delegate some power to an elected government headed by Hassan Rouhani, the reformist president.
"The previous regime thought monarchical rule would last forever, but it lost everything for this very reason - that it did not hear the criticism of the people," he said recently, referring to the ousted Shah of Iran.
Iran's government has a long history of successfully suppressing dissent and it is not clear how far the protests will go.
But Sotoudeh said she expects there is still more to come. "This is an ongoing protest and more women are joining in every day. They cannot arrest all of them."
