One of the victims has been identified as Nargis, 25, while the other is a man of about 42 years of age whose identity is yet to be confirmed, police say.
Doctors declared them dead after they were brought to the emergency ward of the Dhaka Medical College Hospital (DMCH) in the early hours of the day.
Three children 'from the street' brought Nargis to the hospital when she was found lying injured on a road near Khilgaon Taltola market, said Md Bachchu Mia, officer in charge of DMCH's police outpost, quoting the children.
Police have learned the woman was homeless.
Meanwhile, Hazaribagh Police Station Sub Inspector Ranjit Ghosh said locals found a man injured in the Beribadh Bow Bazar area at 3 am.
The man succumbed to his injuries as police, after being informed of the matter, took him to DMCH.
SI Ranjit said police are trying to identify the man and find the vehicle that caused his death.