"They phoned in; we thought it was a joke," Mr Moore said.
Police came shortly after and closed off the 10th fairway as they checked the car to make sure there was not a body inside.
Contractors removed the car by 9.30am.
Mr Moore said the club had video footage of the car passing a shed and that would be provided to police.
One of the club members who lived by the course heard what he later realised were the car's tyres exploding about 3.45am.
That fitted with the timing of the footage on the video camera.
The fairway was left with "a big burned out patch", but no other serious damage.
"We're thankful it was done away from trees and no damage was done to the greens.
"But it's a bit sad really.
"You can't control what people decide to do."
Police said the car was stolen from Tedder St in St Kilda. It had been driven through a chain on the golf course.
Police removed a petrol can from the scene, which was left by the offender.
The incident follows a string of car fires in July, including one burned at the Chisholm Park Golf Course and another set alight at nearby Kettle Park.
There was also a string of fires in March.
Police said then it was possible parts were being stolen from the cars before what remained was set alight to hide evidence.