The new law - the Hindu Marriage Registration Bill 2012 - aims to provide legal and social protection to members of the Hindu community.
State Minister for Law, Justice and parliamentary Affairs Qamrul Islam moved the bill that was passed by voice vote, bdnews24.Com reported.
The bill was placed in parliament on July 3.
He said the law was being formulated since there was no such law in the country to register the marriages of Hindus.
The minister said the marriage of a Hindu couple is held under religious customs and so has no documents.
"Due to absence of documented evidence both parties especially the Hindu women are subjected to cheating,"he said.
The law would authorise the government and the local government authorities to appoint a marriage registrar to be known as Hindu Marriage Registrar at every ward of the city corporation and municipality.
The bride would have to be minimum 18 years old and the groom 21 years, the report said.