Police say he is being held after the discovery of evidence linking him to a conspiracy to murder the son of Prime Minister Sheikh Hasina.
The leader of the opposition Bangladesh Nationalist party, Khaleda Zia, demanded his unconditional release.
Mr Rehman is the third pro-opposition editor to be detained in recent months.
The editors of the leading Bengali and English newspapers have both recently been accused of similar crimes.
Mahfuz Anam, editor of the respected English-language Daily Star newspaper, faces charges of treason for accusing Prime Minister Sheikh Hasina of corruption in 2007 when the country was run by a military government.
Freedom of press 'under threat' in Bangladesh
The prime minister's son, Sajeeb Wazed Joy, has claimed that the articles were an attempt by Mr Anam and the Daily Star to "support a military dictatorship in an attempt to remove my mother from politics".
Similar allegations are now being levelled against Mr Rehman, 81, who was arrested by plain-clothed policeman on Saturday morning.
He was at one time the speech writer for Khaleda Zia, the prime minister's arch-rival.
"He has been arrested over sedition charges filed by police in Dhaka in August 2015," police spokesman Maruf Hossain Sorder told the AFP news agency.
Mr Rehman was the long-time editor of Jai Jai Din, a mass-circulation Bengali daily. He now edits a popular Bengali monthly magazine called Mouchake Dhil.
In recent months Mr Rehman convened the international affairs committee of the BNP and headed a  pro-opposition think-tank called G-9.
BBC South Asia correspondent Justin Rowlatt reported in February that both The Daily Star and its sister publication Prothom Alo - the most widely read Bengali newspaper in the country - are being subjected to a clandestine attempt to undermine their finances and stifle their operations.
The latest media uncertainty comes amid growing concern about freedom of speech in Muslim-majority Bangladesh, which in recent months has suffered a series of Islamist killings of secular bloggers and publishers.
Prominent Bangladeshi magazine editor Shafik Rehman has been arrested in Dhaka on suspicion of sedition, police and his family have said.