Federation Internationale de Football Association said Tuesday it was "aware of that tragedy and deeply regret it".
Esteghlal issued a statement, offering condolences to Ms Khodayari's family.
The 30-year-old set herself on fire last week after reportedly learning she may face between six months to two years in prison.
Separately, the state-run Iran newspaper reported that the vice president for women and family affairs, Masoumeh Ebtekar, had asked the judiciary to look into the case in a letter.
Iranian women cheer as they wave their country's flag after authorities in a rare move allowed a select group of women into Azadi stadium to watch a friendly soccer match in 2018 (file picture). Iran's government faced an August 31 dead by Fifa to allow women to attend official football matches in order to "pave the way" for female attendees, the BBC previously reported.
Her death sparked an outcry on social media, with some Iranian users blaming the stadium ban and the actions of the court and police for her death. According to Human Rights Watch, this unofficial prohibition has barred women from entering stadiums since 1981.
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The attack that took several lives was claimed by the Taliban. Marine General Kenneth McKenzie, the head of U.S. Barreto Ortiz, 34, last Thursday.
She had tried to sneak into the stadium dressed as a man, her sister previously told Iranian media, but admitted she was a woman when security tried to search her.
"We are all responsible", Iranian lawmaker Parvaneh Salahshouri wrote on Twitter, saying that Khodayari "wasn't just the 'Blue Girl.' She was Iran's girl, from a country where men decide what women should or shouldn't do".
The Iranian sports ministry said last month that women fans would be allowed into the stadium when Team Melli - as the national team are known - play their next home qualifier.
"We had presented the medical documents to the court, but she was treated as a healthy person after she insulted one of the officers", the sister said.
"This discriminatory ban must end immediately and the global community, including football's world governing body, FIFA, and the Asian Football Confederation, must take urgent action to end the ban and to ensure that women are allowed access to all sports stadiums without discrimination or risk of prosecution or punishment", he said.
The stadium ban has not been written into law or regulation, but it has been performed by this Asian country.
Iranian football legend Ali Karimi urged his 4.5 million Instagram followers to boycott stadiums until further notice.