The incident happened about 3.30pm on Malaghans Rd, when a silver Volvo allegedly hit a man riding a motorised bike with a 3-year-old boy on the back.
Senior Sergeant Blair Duffy, of Queenstown, said an off-duty Queensland police officer witnessed the incident.
When the driver of the silver car failed to stop the visiting policeman gave chase, ultimately finding the car and calling Queenstown police.
The man and child, believed to be local residents, received minor injuries and were treated at the scene by St John Ambulance.
After inspection, Snr Sgt Duffy said the bike would probably need replacing.
Speaking to the Otago Daily Times at the scene, he said it was believed the driver of the vehicle was from the United States.
Police investigations were continuing.
"We've got the driver of the vehicle involved and taken him back to the station for questioning. We are examining that motor vehicle to establish the cause of the crash.''
The relationship between the child and the man was unknown.
However, the boy's father arrived at the scene soon after emergency services. He declined to comment on the incident.
