The man was filmed wielding the axe just before 12pm Tuesday at the intersection of Glynburn and Magill Roads at Kensington Gardens.
The man steps out of his car with the weapon and starts hitting a road bike before threatening the cyclist.
Shaken, the cyclist steps back.
Danny, who witnessed and filmed the incident, told 7 News the duo came to blows after the cyclist started hurling abuse at the driver before banging on the passenger window and smashing the motorist’s side mirror.
“I could see a cyclist punching the car window non-stop,” Danny said.
“One hundred metres down the road he’s still punching the window of this old guy’s car and then he busted the guy’s mirror.”
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Danny thought the pair were about to have a fight until the man stepped out carrying an axe and “went to town” on the cyclist’s bike.
He said the two men then went their separate ways.
Police are investigating the altercation and no charges have been laid.
Officers said they are urging the two men and anyone who witnessed the incident to come forward.
Anyone with information can contact Crime Stoppers on 1800 333 000 or use the Crime Stoppers online reporting page.