"The board has been dissolved as most members have resigned voluntarily," the sports ministry said in a statement.
"It is hoped that the interim committee will soon take up charges and will take steps to organise a permanent committee."
Jamali, chief of general staff of the Bangladesh army, will head an interim committee that includes Fahim Munaim, principal press secretary of Fakhruddin Ahmed who is head of the army-backed interim government.
Industrialist Salman Ispahani, a leading sports organiser, is the only member of the dissolved 31-member board to be included on the interim committee.
Seventeen board members, including general secretary Mahbub Anam and vice-president Gazi Golam Dastagir, resigned last week following the interim government's plans to depoliticise the governing body.
The authorities had criticised most board members for being linked to major political parties, which they said jeopardised the normal running of the game.
Abdul Aziz, a government bureaucrat and president of the dissolved board, was excluded from the interim committee having recommended that the vacant posts should be filled.