South Yorkshire Police says one of its cars was travelling with its lights and siren on yesterday (Tuesday, March 14), at around 7.55am, when it was involved with a black Peugeot 5008.
The Peugeot then collided with a cyclist waiting at the lights between Queens Road and Charlotte Road.
The driver of the Peugeot and the cyclist were not hurt in the collision, police said, but an officer in the police car was taken to Northern General Hospital with minor injuries.
Police say they have dash cam footage of the collision from their vehicle but want to speak to anyone who witnessed the incident.
Anyone with information is asked to call police on 101, quoting incident number 172 of March 14.