The 1898 Lepers Act was passed at a time the authorities believed leprosy was highly contagious. Officials now say the law contravenes human rights.
Correspondents say lepers currently face arrest and a fine if they venture out of their care centres.
Government estimates suggest Bangladesh has about 40,000 leprosy patients.
They have been denied job opportunities and are not allowed to use the public transport system, our correspondent says.
Activists say the move will help integrate patients into society and that from now on leprosy patients can get access to health care in all hospitals.
Activists believe the number of people who have leprosy is higher than official figures suggest, as many people do not report the condition because of the social stigma associated with it.
But now that the government has repealed the law, they hope sufferers will be encouraged to come forward for treatment.