Video footage shows the men throwing punches and kicking each other in the middle of the intersection at Elizabeth and Goulburn Streets around 12.40pm today.
Two passers-by eventually stepped in to separate the men and stop the fight.
NSW Police said the 47-year-old van driver and 53-year-old bus driver were involved in an altercation following an earlier alleged road rage incident.
“The 47-year-old fled the scene. The 53-year-old was taken to hospital suffering facial injuries,” NSW Police said in a statement.
Police are investigating the incident.
Any witnesses have been urged to contact authorities.