The reason? Her husband barred her from leaving the country.
The reaction on social media was swift, and many Iranians vented their fury by demanding the government change the law to give women back their right to travel internationally, along with other rights stripped away after they're married.
Based on domestic family law in the Islamic Republic, women give up the right to leave the country, pursue education or even choose where to live and work upon signing a marriage document. The only exception is if a woman's husband relinquishes those rights, which rarely happens.
The only rights married women retain are limited custody of children and the right to divorce.
Zargari's case, however, went viral and different hashtags about women's rights began popping up on social media, including the "right to leave the country" and "no to discrimination against women."
When asked to comment on Zargari's case, the International Ski federation provided ABC News with a statement but did not mention Zargari by name.
"FIS sympathizes with any team member who is not able to travel to our World Championships," the statement read. "However, FIS is also not in a position to dispute the laws of any given nation."
Zahra Abdi, an Iranian poet, wrote on Twitter: "It is impossible for a society to move towards the future when the hands and feet of half the people are tied up. This is well understood by the developed countries and it is why they fight discriminatory laws against women. Wherever there is a sign of development, this struggle is taken more seriously."
An online campaign asking to revise regulations on women leaving the country was signed by almost 50,000 people in less than a week.
"The basis of the family law in Iran is that the husband has all the rights," an Iranian lawyer, who requested anonymity out of fear of reprisal, told ABC News. "Any woman who wants any of the rights back has to swim against the river and prove it at the court."
Despite the outcry, the Iranian government hasn't budged.
Responding to the social media campaign, Masoumeh Ebtekar, vice president for Women and Family Affairs, tweeted that in an emergency, women can ask the court to revise a husband's decision but this can only happen after a judge is convinced the travel is "necessary," and, even then, the woman would only be allowed to leave "on bail."
The Iranian lawyer said that a bill addressing the travel issue is making its way through government, but it first has to be passed by the parliament, and the language, as it currently stands, is very "vague" when addressing how exactly judges would deem travel necessary. The lack of clarity also may delay any movement on the bill.
"Basically," the lawyer told ABC News, "the 'necessity' mentioned in the bill is based on the need for medical treatment out of the country, attending scientific conferences and, more recently, attending sport events like international championships."
In one of the first reactions to the issue, Zargari wrote in a story on her Instagram page that her husband was born in the United States and was not raised in Iran, seeming to imply that discriminatory laws remain in place regardless of a person's citizenship.
However, when she later told the Iranian Students News Agency in an interview that government officials should "at least remove this law for women champions and those who are active in the international fields," a huge backlash was sparked, this time against Zargari. Many who supported her on social media during her ordeal began to criticize her for not standing up for all women -- not just those who work internationally.
"Unfortunately, Ms. Zargari has said that she hopes the law that needs husbands' permission for leaving the country is removed for women who work in the international fields. The right thing to say would be that this law is cruel and humiliating and medieval, and no woman needs her husband's 'permission' to travel," journalist Yosra Bakhakh tweeted.
Explaining how such social media campaigns can help return these rights to women, the Iranian lawyer referred to the ambiguities of the law that could result in minimal reforms.
"For example, it is up to the common sense in the court what 'necessity' means for a woman's demand to leave the country. In the past, traveling abroad to attend sport events would not be a case of necessity. But, thanks to all activism through the years, it has become so. It matters that people would not stop asking for more," she said.
It is clear, however, that women's rights activists are paying an enormous price to achieve equality.
Just last week, Najmeh Vahedi, a sociologist, and Hoda Amid, a lawyer, who held workshops to tell women how to preserve their rights upon marriage, were sentenced to seven and eight years imprisonment, respectively.