Police and witnesses said BNP and its youth front brought out a procession from Narayanganj's Kumudini Welfare Trust around 6am. When police tried to stop them, pitched battles erupted.
Narayanganj Sadar police station OC Monjur Kader said police had to fire in the air to disperse the BNP supporters.
Witnesses said at least five people were injured in the clashes.
Similar clashes also took place at Chasharah at around 6:30am. Another five were injured.
OC Kader said they had detained 21 persons in the morning during raids in various parts of the city.
The opposition alliance called for the 36-hour shutdown protesting against the jailing of top BNP leaders.