Gaibandha Superintendent of Police (SP) Ashraful Islam told a media on Thursday that one Anwarul Islam Rana has been arrested in Dhaka.
The 27-year-old, a resident of the district's Sundarganj Upazila, has confessed to have taken part in the killing of the ruling MP, Islam told reporters in Gaibandha.
He is being transported to Gaibandha, said the senior police officer.
On the evening of Dec 31, unidentified assailants shot the ruling party MP from Gaibandha-1 (Sundarganj) constituency at his home several times. He died an hour later at a hospital in Rangpur
On Tuesday, police arrested former Jatiya Party MP Adbul Kader Khan of the same constituency from his home in Bogra City and secured a 10-day remand the next day to interrogate him.
MP Liton's family started a case with the Sundarganj police over the killing accusing five unidentified men.
Police have so far made 28 arrests, including former lawmaker Kader.