Dodd had previously been a co-opted member of FIFA's old executive committee and was a leading voice promoting women's football within the global body.
Ahkter beat Dodd by 27 votes to 17 after two other candidates for the woman's slot representing Asia on the FIFA Council withdrew before the ballot.
"Naturally it is disappointing. I'd hoped I had done enough in the few years I was part of FIFA to persuade people that I should have another shot at it," Dodd told reporters.
"I think I will always be an advocate for women's football...here are still a lot of ways to contribute. I am still a member of the AFC executive committee and of the board in Australia and I have other involvements," she added.
Australia has only been a part of the AFC since 2006 having previously been in the Oceania confederation and Dodd's loss could be viewed as an indication of the country's political weakness in Asian football.
"My vote was with @moyadodd. This is very disappointing," American Carli Lloyd, twice women's world player of the year, said on Twitter.
Ahkter is a member of the AFC's executive committee and women's football committee.
"This is like a dream come true," she said. "I've always wanted to do something for Asian women's football. Now I have the platform to do something."
Dodd, a former Australia national team player, was looking to regain her place in the FIFA leadership after her spell as a co-opted member of the old executive ended with the creation of the new FIFA Council in 2016.
The candidates for the three available Asian positions on the FIFA Council were all elected unopposed with Chinese Football Association general secretary Zhang Jian, South Korea's Chung Mong-gyu and Mariana V Araneta Jr of the Philippines all joining FIFA's ruling body.
Olympic Council of Asia president Sheikh Ahmad withdrew from the elections after he stood down from all football positions following reports linking him with a U.S Department of Justice investigation into bribery.
Sheikh Ahmad has denied any wrongdoing.
FIFA is holding its congress in the Bahraini capital on Thursday.
(Editing by John O'Brien)
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