Police were told the driver of a grey Subaru was seen driving dangerously and wielding a meat cleaver toward other drivers northbound on the bridge at about 6.16pm yesterday.
The knife was dropped on the road and has been seized by police.
According to 2GB, police said the incident may be linked to a similar outburst of road rage near Barangaroo on Monday night.
That involved a man attacking an Uber driver, damaging his car.
Anybody with information is urged to contact Crime Stoppers on 1800 333 000.
