Emergency services were called to Barnards Avenue at Hurstville, in the city's south, following reports of a car fire just before midnight on Monday.
Officers found a white Mercedes-AMG convertible well alight.
Fire and Rescue NSW put out the blaze, but the car was destroyed.
The house sustained minor damage after the fire spread to an upstairs room.
The white Mercedes was set alight twice in three days. (Bianca De Marchi/AAP PHOTOS)
Superintendent Chris Hill said it was the second incident involving the same family and vehicle in a few days.
"Clearly the incidents are targeted and of a suspicious nature," he said on Tuesday.
Images from the scene show the white Mercedes-AMG, which costs more than $200,000 when new, parked next to a black luxury SUV from the same marque.
"At this point in time, motive remains a mystery to us," Supt Hill said.
The white Mercedes was previously set alight in the driveway about 1am on Friday.
The fire went out and caused minor damage to the vehicle.
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