The punishment was meted out Saturday to the 30-year-old man by the local council in a village 30 kilometres (18 miles) south of Dhaka.
Police said he had kidnapped and then forcibly married a 12-year-old girl, who later managed to escape.
"The council chief and some village elders beat him and made him parade with a brick tied to his penis at a river ghat (steps) under the full gaze of at least 200 people," police sub-inspector Binoy Krishna Kar said.
Village courts are legal in Bangladesh but only empowered to settle disputes related to land ownership, inheritance and other minor issues. They are proscribed from handing down physical punishment.
The latest incident came a week after the global rights monitor Human Rights Watch released a statement highlighting abuses committed by local councils which are often the result of religious edicts or fatwas.
The group urged Bangladesh, a Muslim-majority nation of 142 million people, to take "urgent" measures to prevent such cases, which have been blamed for the deaths of dozens of women in recent years.