The female cyclist was riding along Anlaby Road near Newington Health Centre when the taxi stopped.
The passenger door of the taxi was opened and the cyclist collided with it and fell off her bicycle.
The taxi’s passenger stayed at the scene but the taxi driver drove off.
An ambulance crew was called to the scene and the woman was taken to hospital.
A spokesperson for Humberside Police said officers wanted to trace the taxi driver who may not have known they had been involved in a collision.
The accident occurred at around 5.30pm on Monday.
Anyone who has any details about the taxi or its driver, or saw what happened, is asked to contact the force on 101 quoting log 463 of May 14.