Shahbagh police said they recovered an unidentified woman in an unconscious state from the footpath in front of Salimullah Muslim Hall at the University of Dhaka on Tuesday morning.
Sub-Inspector Liton Ali said police acted after receiving information from the area.
He said the woman was taken to the emergency department of Dhaka Medical College Hospital, where a doctor declared her dead after an examination.
Police sent the body to the hospital at about 10:15am.
Police described the woman as about 60 years old and said her identity had not been established.
Liton Ali said inquiries with local people did not establish her name or address.
Police said they were seeking to identify her through biometric and other technological means.
The body was kept in the hospital morgue while legal procedures continued, police said.