Mahfuza Akhter Kiron, a Fifa Council member, was detained after she had said that Prime Minister Sheikh Hasina was neglecting football.
A defamation claim was then filed by a local sport official, alleging that the comments embarrassed the entire nation.
On Saturday, Ms Kiron was denied bail and sent to jail, her lawyer said.
“We sought bail for her after she was taken to the court. But our prayer was rejected,” her lawyer Liakat Hossain said.
The government of Sheikh Hasina has been accused by human rights groups of using tough media laws to stifle dissent in the country.
Last August, renowned Bangladeshi photographer and activist Shahidul Alam was jailed for “spreading false information” during mass demonstrations.
What did Mahfuz Akhter Kiron say?
During a recent TV talk show, Ms Kiron said that Prime Minister Sheikh Hasina was neglecting football in the cricket-mad Bangladesh.
This prompted local sport official Abul Hasan Chowdhury Prince to file a defamation claim.
“Mahfuza told the TV show that [the] PM maintains double standard for football and cricket. She rewards cricket for personal gain but ignores football,” Mr Hasan’s lawyer was quoted as saying by the Associated Press.
The defamation claim alleges that such comments about the sports-loving prime minister embarrasses the entire nation.
Prime Minister Sheikh Hasina – who last December secured her third consecutive term in office – has so far made no public comment on the issue.
In 2017, Ms Kiron was elected Fifa’s female representative for Asian football.
She was soon facing strong criticism for struggling to name the current women’s world champions – the US team.