According to his newspaper, Prothom Alo, Shamsuzzaman Shams was picked up from his home in the industrial town of Savar just outside Dhaka at around 4 am.
Rights groups say the Digital Security Act under which Shams was charged has been widely used by the government to muzzle journalists and critics.
The article by the Prothom Alo was published on Sunday and included quotes from ordinary people talking about their lives on the occasion of Bangladesh's independence day.
What is the use of this freedom if we can't afford rice? One labourer was quoted as saying.
Since Russia invaded Ukraine, the cost of food has gone up in Bangladesh since the middle of 2022. Its currency, the taka, has fallen sharply against the US dollar.
The home minister, Asaduzzaman Khan, confirmed that the reporter was questioned by police for a false story published at the weekend.
The minister said that Shams would be released from custody, but could be arrested over the charges after a case was filed against him.
According to a case file obtained by Agence France-Presse, the reporter was charged with smearing the image of the government with false news and raising questions about the achievements of Bangladesh under the Digital Security Act.
Nearly 3,000 people have been charged with being indicted under the Digital Security Act since it was enacted in 2018, including about 280 journalists, according to a local thinktank.
This has resulted in concerns that the South Asian nation of 170 million people is becoming increasingly authoritarian under prime minister Sheikh Hasina, who has been in power since 2009.
Reporters Without Borders ranked Bangladesh 162 of 180 countries in its 2022 World Press Freedom Index. In the last few months, Bangladesh's dwindling number of independent media and journalists has come under increasing attack by the government and Hasina s ruling party.
The authorities shut down the lone opposition mouthpiece in February, saying it was in violation of the country's press laws.
At least 10 journalists were beaten up by police while covering a disputed election of supreme court lawyers in Dhaka.