The 1-0 victory over South Korea at Tehran's 100,000-seater Azadi Stadium was held on the first of two mourning days on the Shia Muslim calendar.
Fifa said the £37,000 fine relates to "several religious manifestations".
World football's governing body prohibits political, religious or commercial messages at matches.
Fifa also punished the Croatian and Kosovan football federations over fans' anti-Serb chanting during their World Cup qualifier on 6 October.
Kosovo's membership of Fifa was opposed by Serbia, from which it declared independence in 2008.
Croatia were fined £41,000 and Kosovo £25,000. Croatia won the match - Kosovo's first competitive home fixture - 6-0.
Read more: What is Ashura?
Iran have been fined by Fifa after fans were asked to sing religious chants and wear black at a World Cup qualifier played on a holy day in the country.