The accident on Friday morning at Misonparha area left another child injured.
Police identified the victims as Shirin Akter, 28, and her four-year-old daughter 'Joyeeta'. Her other daughter, 'Arpita', 12, have been admitted to the Narayanganj Sadar Hospital.
Narayanganj Sadar Model Police's OC Manjur Kader said a wheat-laden truck struck a rickshaw, killing Shirin and her daughter on the spot.
Locals blocked the road, vandalised the truck before torching it.
They fought pitched battles with police as the law-keepers tried to take control of the situation resulting in a traffic snarl lasting an hour.
Vehicular movement resumed after police dispersed the agitated locals around noon.