The vegetarian Indian leader arrived on Tuesday in the Bangladeshi capital Dhaka on an official visit aimed at boosting the sometimes fraught relations between India and its smaller Muslim-majority neighbour.
Hilsa fish will be on the menu for official functions during the Indian prime minister's visit, Bangladeshi officials said, although both Singh and his wife are vegetarians.
Hilsa is a Bengali delicacy and one of the most popular dishes for the some 250 million Bengalis who live in both Bangladesh and the eastern Indian state of West Bengal.
"I am willing to break my vegetarian vow because I have heard about the delicious dish of hilsa fish. So I am willing to make that exception," Singh was quoted as saying by a Bangladesh news agency ahead of his arrival.
Many Indians are vegetarian but Singh's Sikh religion does not require him to be one.
Although hilsa are also caught in the rivers of West Bengal and in the western Indian state of Gujarat, the varieties from Bangladesh are considered more delicious.
In recent years, Bangladesh has set a minimum price for hilsa meant for export to India -- seen as a tit-for-tat move by Dhaka after India was accused of slapping non-tariff barriers on Bangladeshi goods.
In West Bengal, hilsa is a must for festivities, and is especially popular for a festival called Jamai Shasti -- or the Son-in-Law Day -- when families treat their son-in-law with the fish which is either fried, steamed or smoked.