Chief Justice Obaidul Hassan resigned, a law ministry official said on the condition of anonymity, after students warned him of "dire consequences" if he did not. Reuters could not immediately contact Hassan.
Bangladesh Bank Governor Abdur Rouf Talukder has also resigned but his resignation has not been accepted given the importance of the position, finance ministry adviser Salehuddin Ahmed told reporters. Reuters could not contact Talukder.
Days earlier, four deputy governors were forced to resign by 300 to 400 bank officials accusing them of corruption.
Hasina has been sheltering in New Delhi since Monday following an uprising that killed about 300 people, many of them students, ending her uninterrupted rule of 15 years in the South Asian nation of 170 million people.