New Delhi has told Dhaka that the dam on the Borak River in Manipur state would produce electricity and control flooding in both north-eastern India and Bangladesh.
Manipur authorities have signed a deal with hydropower developer Satluj Jal Vidyut Nigam Ltd and the National Hydroelectric Power Corporation of India for the dam.
Bangladeshi experts said they feared the dam at Tipaimukh could cause desertification along the Borak, Surma and Kushiara rivers.
The main opposition Bangladesh Nationalist Party launched a week-long protest against the dam, which would take more than seven years to construct.