Aman is the first member of the cabinet of Khaleda Zia, a former prime minister, to be convicted for corruption since the army-backed interim administration began the drive.
The court ordered Aman to pay a fine of $14,500 or serve another year in jail. The couple's assets have been confiscated.
More than 170 political figures including Tareque Rahman, Khaleda's elder son and political heir, have been detained in the anti-corruption hunt aimed at cleaning up politics before elections expected late next year.
The special court last month sentenced an aide of Khaleda and the owner of a private television channel for extortion.
Bangladesh is under a state of emergency imposed after political violence late last year.
An election scheduled for January 22 was cancelled and all political activity banned.