After calls for Iran to be banned from the 2022 World Cup because of the continued exclusion of women from football matches in the Islamic republic, Infantino adopted a policy of personal engagement with the country's leadership.
Monday's Pro League clash at Isfahan's Naqsh-e Jahan Stadium, which home team Sepahan won 2-1, was played in front of a crowd made up exclusively of women and girls.
That decision came after a Sepahan cheerleader led insulting chants about female Persepolis fans at a previous clash between the clubs at Tehran's Azadi Stadium in May.
The Iranian Football Federation fined both clubs and ordered their next two meetings be played in front of only female fans.
In comments posted by FIFA on social media, Infantino said he was "very pleased" that some 45,000 women and girls had been allowed to attend the latest edition of one of Iran's fiercest club rivalries.
"FIFA has been in constant contact with authorities in IR Iran for several years regarding women and girls having the possibility to attend football matches," the Swiss said.
"After last year's Tehran derby between Persepolis and Esteghlal where 3,000 women and girls were in attendance, this latest development comes as a glowing representation of how our game is inclusive and open for everyone to enjoy.
"I would like to express my heartfelt gratitude to all concerned who made this possible."
Open Stadiums, the women's rights campaign group that led the calls for Iran to be excluded from the World Cup, said the fans had turned the stadium "into a symbol of defiance".
"Women's access to stadium capacities remains very limited," it said in a social media post after the match.
"Today, as a punishment for male fans, Iran's FA allowed only women to attend, and Sepahan Stadium was nearly full. The road to equal and normal access to stadiums for Iranians still requires significant attention."
