Lt Col Chaliao Taihoo of the Phuket City Police was notified at 4:30am.
At the scene, on the northbound lanes near the Shell petrol station, officers found a grey Bangkok-registered Honda car overturned in the drainage ditch in the middle of the road.
The two male passengers in the car were reported as having minor injuries from the accident and the driver was reported as suffering no injuries at all.
The passengers, one with an injury to his right hand and the other with an injury to his right eyebrow, were taken to Bangkok Hospital Phuket, police reported.
The driver, who police did not report as foreign or Thai, was taken to Phuket City Police Station for questioning.
No other details were made available by police, who said they were continuing their investigation.