Officers were called to Arundel Gate at around 12.10pm following reports that a man had been hit by a van.
Arundel Gate was closed for around half an hour as police dealt with the incident.
Stagecoach Yorkshire reported that there was "major disruption and delays" to bus services leaving the city centre due to the road being closed.
Travel South Yorkshire said that, due to the incident, all services were subject to delays and possible short notice diversion.
The road reopened at around 12.45 and Stagecoach Yorkshire said buses were back to their normal routes but warned commuters to expect heavy delays across most routes.
Police said that the pedestrian was not injured in the crash.