Abu Tayeb is the Khulna correspondent of private television channel ntv and the daily Loksamaj.
The journalist was arrested from his Khulna home Tuesday, hours after city Mayor Talukder Abdul Khalek filed the case against him.
The mayor in the case statement alleged that Abu Tayeb deliberately circulated misinformation against him on Facebook multiple times.
A day after his arrest, a Khulna court sent him to jail.
In Joypurhat, a court yesterday sent Md Amanullah Aman to jail in the other DSA case.
The 19-year-old accused is a resident of Moddhopara village in Kalai upazila.
Police said a local Chhatra League leader recently in a Facebook post welcomed the arrests of some Hefajat-e-Islam leaders.