The bystander, aged in his 80s, suffered injuries following the public order incident on Patrick Street in the city.
Video footage of the fight shows two men trading blows before grappling one another on the ground.
Gardaí are carrying out investigations into the incident but no arrests have yet been made.
Emergency services were alerted to the scene on Patrick Street shortly before 8pm after receiving reports of two men fighting on the busy road.
When they arrived the suspects had fled but they discovered a man in his 80s had suffered non-life threatening injuries.
The wounded pensioner was an innocent bystander and suffered injuries to his hand after being pushed to the ground during the fight.
He was brought to hospital for treatment and gardaí are continuing their inquiries into the incident.
Footage of the incident, shared by Red FM’s Neil Prendeville, shows two men punching one another on the busy road as cars pass by.
Several people look on as the men grapple with one another before one suspect puts the other in a headlock and drags him to the ground.
A Garda spokesman said: “Gardaí were called to a reported public order incident on the 6th June 2022 at 7.55pm.
“Gardaí arrived at the scene and the suspects were gone on arrival. A man in his 80s suffered non-life threatening injuries during this incident and was conveyed to the Mercy University Hospital for treatment.
“No arrests have been made. Investigations are ongoing,” the spokesman added.
Concerns have recently been raised about growing instances of violence across Cork with senior gardaí describing it as “worrying”.
Figures from the local Joint Policing Committee (JPC) show that in the first four months of the year, 98 serious assaults were recorded in the Cork city division.
This compares to 47 such crimes reported in the same period in 2021.
The number of minor assaults also increased from 195 in the first four months of last year to 309, between January and April of 2022.
Similar increases in assaults were recorded in other areas of Cork.
It was reported that Chief Superintendent Con Cadogan, in charge of policing for the county, described it as “worrying”.
“Our assaults are on the increase again. That is a worrying trend. Our serious and minor assaults have increased quite significantly,” the senior garda told last month’s meeting.