Mahmudur Rahman, the editor of the Bengali-language Amar Desh newspaper was arrested during a raid on his office in Dhaka.
He faces charges including sedition and unlawful publication of a conversation that led to the resignation of the head judge of a war crimes tribunal.
The government has also accused Amar Desh of inciting violence.
But Islamist groups staged a street protest on Thursday against his arrest, describing him a "courageous and true soldier of Islam".
Mr Rahman has been remanded in custody by a Dhaka court for 13 days to allow police more time to interrogate him.
"We have arrested [Mr Rahman] in a case filed against him in December," a Dhaka police spokesman told local media.
He said that that the editor is suspected of "publishing false and derogatory information that [has] incited religious tension".
Mr Rahman has been accused by the governing Awami League of using his newspaper to encourage political demonstrations against a war crimes tribunal set up by the government to examine abuses allegedly committed by people who supported Pakistan during Bangladesh's independence war of 1971.
The Awami League says that he has falsely portrayed the government as being anti-Islamic.
"Mahmudur Rahman has hurt Muslim religious sentiments, which is totally unacceptable. He has been arrested to establish the rule of law," state minister for home Shamsul Haque Tuku told local media.
In December the presiding judge of a special tribunal looking into alleged crimes against humanity during the independence war resigned - citing "personal reasons" - after his private emails and Skype conversations were leaked to papers including Amar Desh.
The emails appeared to show that judge Nizamul Huq had discussed the working of the tribunal with a Belgian-based Bangladeshi lawyer.
The opposition has argued that it was improper for a judge to discuss the case with outsiders, but the government has insisted that he was not acting injudiciously and that sections of the media were "attempting to besmirch" the country's reputation.