The accident occurs in the Nobboi Degree area on Udaypur Road
Dhaka's two city corporations have been instructed to remove garbage only in covered vans and between 10pm and 6am.
Bangladesh's capital city of 18 million residents produces up to 5,000 tonnes of garbage a day, according to data provided by city authorities.
Justice Quazi Reza-Ul-Hoque and Justice Mohammad Ullah gave the order on Monday after a preliminary hearing on a writ petition.