The proposals are in a bill likely to be approved by parliament.
It is suggested that the marriageable age for men be reduced from 21 to 18 and for women from 18 to 16.
The maximum penalty for breaking the law will be increased from two months in jail to two years.
The fine, currently $130 will go up five-fold.
Observers say the measures are aimed at combating child marriage, which is widespread in rural Bangladesh.
“Those who marry [underage], conduct such marriages, and the parents will be liable for punishment,” Cabinet Secretary Muhammad Musharraf Hossain Bhuiyan was quoted by local media as saying.
“But women will not be sentenced to a prison term.”
Bangladesh has one of the highest rates of child marriage in the world, with 20% of girls becoming wives before 15 years old.
Aid agencies have described the practice as a “new kind of slavery”, made worse by the fact that some in the country see girls as a burden who do not earn an income.
The girls are totally dependent on their families to support, protect them and pay their dowries.
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