Sirajum Munira, 28, was arrested under the South Asian country's controversial digital security laws over her social media post.
"She posted a derogatory comment on the death of [former health minister] Mohammad Nasim. She mocked a dead person," local police chief Rabiul Islam told AFP news agency.
"It [the post] went viral and created negative reactions and undermined the image of the country," Islam added.
Munira, a lecturer at northern Begum Rokeya University, later apologized and deleted her Facebook comments.
"On Sunday, Munira's bail appeal was rejected by a judge, who sent her to jail. The next hearing is scheduled on Monday," said Harun Ur Rashid Swapan, DW's correspondent in Dhaka.
Controversial internet laws
Bangladeshi authorities have arrested at least 44 people since March under internet laws for allegedly spreading rumor and propaganda amid the coronavirus pandemic.
Rights activists say internet laws in Bangladesh are being used to suppress dissent and target those who criticize the government's handling of COVID-19.
Section 32 of the Digital Security Act 2018 considers the secret recording of any information at any government, semi-government or autonomous institutions as espionage. Many journalists and online activists, who expose government corruption by secretly recording irregularities, fear that their work can also be regarded as espionage.
If convicted for violating the provision, a person may face imprisonment of up to 14 years and a fine of about €20,000 ($22,510) under the law.
Spike in cases
Bangladesh has so far reported nearly 90,000 coronavirus cases and around 1,200 related deaths.
On Sunday, the country reported 3.141 news cases and 32 more COVID-19 deaths.
On Saturday, Sheikh Abdullah, the state minister for religious affairs, died of the coronavirus after being admitted to a military hospital.
Two ministers in Prime Minister Sheikh Hasina's cabinet, as well as five members of parliament, have also been tested positive for COVID-19, a minister told AFP.
Experts say Bangladesh's state-run hospitals are overwhelmed with COVID-19 patients, with many of them being deprived of intensive care beds and ventilators.