He said the law currently allows those accused of rape to "ask questions as to the immoral character of the victim" but this would be banned, with parliament expected to formalise the decision by June.
"This is another step towards empowerment of women," he said.
Prominent activist Nina Goswami of the local Ain o Salish Kendra rights group hailed the move as a "remarkable achievement".
She said character evidence had hindered justice for decades, with many survivors deciding not to seek charges against their attackers out of fear of social humiliation.
"This will now stop," she said.
Last year the Bangladesh Legal Aid and Services Trust (BLAST) said character evidence had been used to cast doubt on victim testimony, making it difficult to secure guilty verdicts.
Rights groups have said the number of rapes has increased alarmingly in recent years, blaming legal loopholes and a culture of impunity for violence against women.
National anger over the issue has boiled over into sustained public protests, as in 2020 when members of the student wing of Hasina's party were arrested and charged in a gang-rape case that outraged the public.