Alinejad has also founded White Wednesdays, a movement which saw many women take off their headscarves in protest of the "discriminatory law".
She says visitors to Iran shouldn't wear the hijab out of "respect for the culture of Iran", and those who do are "sending a message that men are more equal than women".
In a video circulating on Twitter she says: "Iranian women, they fight against the compulsory hijab and they are alone, they are on their own.
"There were three female politicians from the Netherlands - they went to Iran the same day when one of the women of the White Wednesdays movement put her headscarf on a stick and waved it in public, she got arrested.
"The same day there were three female politicians from the Netherlands in Iran obeying compulsory hijab law without challenging it.
"So the female politicians who go and visit Iran, the tourists, athletes, actresses - all of them, when they go to my beautiful country they say that this is a cultural issue, we wear it out of respect to the culture of Iran.
"Let me be clear with you: calling a discriminatory law a part of our culture - this is an insult to a nation."
In her Herald on Sunday column, Heather du Plessis-Allan addressed the rights and wrongs surrounding the issue of wearing a headscarf.
Du Plessis-Allan wrote that a Muslim women's rights advocate in Malaysia suggested that the reason Ardern wore hijab was because she didn't understand the implications. "She is not a Muslim and not from a Muslim majority country," the advocate said in an interview.
Spectator USA took a similar stance, du Plessis-Allan wrote, claiming that being "a self-professed feminist" made Ardern wearing a headscarf even worse.
In summary, du Plessis-Allan wrote that despite the criticism the PM was right to wear a headscarf.
"Putting on the headscarf was the simplest and most compelling way of the Prime Minister telling the Muslim community that they are us and they have our support.
"Supporting all Muslims was more important than being a feminist in the days immediately following the attack."