Brickfields OCPD Asst Comm Ruslan Khalid said the three men were arrested to assist with investigations into the incident.
"We were aware of the incident even before the video went viral.
"We managed to track down those involved and they have since been remanded," he said when contacted Wednesday.
He added that the investigation into the matter is still ongoing.
"Road bullies will not be tolerated as there are laws that must be respected.
"This incident is even more serious as it involves assault with a dangerous weapon," he said.
A two-minute video of the altercation following an accident went viral on social media.
The video starts with the victim parked in front of a shoplot when another car makes a U-turn and hits the victim's car.
The victim gives chase and sounds his horn repeatedly at the other car.
The video then cuts to what looks like a flyover where the alleged assaulter stops his car at a traffic light. The victim also alights from his vehicle to check the damage to this vehicle.
A passenger then gets out from the first car, grabs an object from the driver's side and charges at the victim.
A scuffle ensues out of view of the dashcam.
Facebook user Jimmy Soo posted the video with a caption describing the incident.
"The incident happened on Feb 10 at around 1.18pm while I was waiting in front of a shop at Kuchai Avenue," he said in his post.
He added that they pursued the car for about 400m before they came to a stop at the junction.
"My brother went to inspect the damage when one of the passengers came down from the back and walked towards the driver's side before he started charging at my brother.
"My brother fell to the side and was stabbed by the attacker and I was not spared either. The attacker came around (throwing) punches to my face while I attempted to reason with them," he claimed in his post.
He also posted photos of his brother's stab wound in the thigh, and bruises to his face, as well as a police report.