A 34-year-old man is assisting with police investigations after being involved in an altercation along busy Orchard Road on Friday night.
Police told The Sunday Times they are looking into a case of voluntarily causing hurt.
Videos of the incident, which took place near The Centrepoint mall, were sent to Mandarin television news station Channel 8, and also posted on road safety community page Roads.sg.
It shows two men trading blows as other motorists slowed down and passers-by stopped to look.
Police said they were alerted to the incident at about 10pm.
An eyewitness, quoted in an online report, said the incident started after a man standing by the side of the road used his bag to hit a sport utility vehicle (SUV). After the SUV driver got out of his car, both men started a shoving match.
In an account posted on Roads.sg, a man claiming to be the SUV driver said he had to get out of his car after the man hit the windows.
The writer, identifying himself as Kevin, claimed that the man then hit him with the bag he was carrying, which caused Kevin's spectacles to fall.
"I retrieved a stick from the boot of my car to fend him off," Kevin added. The video shows him hitting the other man with the stick.
Kevin said he told the police he did not want to pursue the matter as he was not hurt.
"My car sustained some scratches and dents, some deep enough to expose the bare metal, but I felt that claiming damages would be more (of a) headache than what the repair was worth," he wrote.