The airline has now given staff the option to opt out of flights to the Iranian capital if they do not want to comply with the rule, which also applies during stop-overs in Saudi Arabia.
Many international carriers have resumed flights to the country since the UK, US and other nations declared it formally safe for travel after an agreement on the government’s nuclear ambitions was struck.
“After decades of isolation, Iran after the nuclear deal is seen as a cool place to visit,” Ms Alinejad.
“The country is being promoted as one of the last placed on earth not to be touched by crass consumerism and commercialism.
“Iran is a beautiful country but let's not kid ourselves, it's not heaven for women. As more people visit Iran, the women in particular will gain a sense of the issue.”
One of the Western tourists who joined the My Stealthy Freedom campaign against Iran's hijab law (AFP/Getty Images)
The campaigner said she had received emails from female tourists from the UK, Belgium, Sweden and other nations saying they had felt uncomfortable being forced to wear the hijab on their holidays.
Many women travelling to the country have already responded to her call to share a “stealthy freedom” photo of themselves with the hashtag #SeeYouInIranWithoutHijab
“I thought it would be easy (to wear the headscarf) but after two weeks, my opinion really changed,” a Belgian woman wrote. “I hated it every minute of the day.”
Another tourist said the restrictions made her “feel like a slaves”, while another woman wrote that she felt unable to express herself.
All the women whose pictures are published on the My Stealthy Freedom Facebook page, which has grown to have almost a million followers in two years, have since left Iran.
One of the Western tourists who joined the My Stealthy Freedom campaign against Iran's hijab law (My Stealthy Freedom)
Asked about the risk women are taking to join the campaign, Ms Alinejad said she believes Western women are less likely to be punished than Iranians.
“Iran wants to attract tourists and in general will turn a blind eye to discretions by them,” she added.
Travel advice issued to British citizens by the Foreign and Commonwealth Office urges visitors to respect Iran’s traditions and laws, while “ensuring actions do not offend”.
It recommends that women wear headscarves in public places, along with trousers or full-length skirts and long-sleeved tunics and coats.
Relationships between non-Muslim men and Muslim women are also illegal, in Iran and punishable by whipping (for the women), although few Westerners have been prosecuted.
Homosexuality, adultery and sex outside of marriage also against Iranian law and can carry the death penalty, while access to Western magazines and films is strictly controlled.