Syed Ashraful Islam was removed due to his "almost regular" absence from meetings of the cabinet.
According to a cabinet statement, the cabinet secretary and overseas welfare minister Khandker Mosharraf Hossain, whose son is married to Hasina's daughter Sayma Wajed Putul, was entrusted with the additional charge of the local government ministry.
"Exercising her authority under the Rules of Business the honourable Prime Minister made the reshuffle in the cabinet," it said.
Islam declined to make any comment to the media.
The development came two days after his absence at a crucial meeting of the Executive Committee of the National Economic Council (ECNEC) reportedly angered the premier while he was previously also criticised by the media for his largely inactive role as a minister.
Hossain earlier declined to comment on speculation that the premier had ordered Islam's removal for his "almost regular" absence from such important meetings.
Islam is a son of the 1971 liberation wartime government's acting president Syed Nazrul Islam.
