Mahfuza Akhter, a FIFA council member since 2017 and national chief of women's soccer, had told a TV talk show last month that Prime Minister Sheikh Hasina had neglected football in the cricket-mad country.
A Dhaka court issued an arrest warrant against Mahfuza on Tuesday after a formal libel complaint from local sports administrator Abul Hasan Chowdhury.
Mahfuza was arrested Saturday morning in the capital, Dhaka police officer Omar Faruk said.
A magistrate in the city's metropolitan court denied her bail application in a hearing later that day, according to Mahfuza's lawyer Liakat Hossain said.
"We sought bail for her after she was taken to the court. But our prayer was rejected," he added.
Bangladesh man jailed for altered Facebook pix of PM
Rights groups have accused the Bangladeshi government of using harsh laws to stifle dissent.
Scores of people have been arrested under strict internet laws and cases have been filed against at least 200 people for making derogatory comments about Hasina online, according to a cybercrime prosecutor.
Mahfuza's arrest came months after Bangladesh arrested and changed award-winning photographer Shahidul Alam with making "false" and "provocative" statements in a televised interview in August.
He was jailed for 107 days -- the photographer said he was badly beaten while in custody -- and denied bail four times before being freed in November.
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