Police were alerted shortly after midnight by several Malmö residents who had heard the loud blast.
Officers eventually located the blown-up vehicle on Fagerstagatan.
The rear-end of the car suffered the most damage. The vehicle was parked in an industrial area south-east of the Möllevången district, with no residential properties on the street.
“We don't know what kind of explosive device it was or if it was just a firecracker pushed down the fuel pipe,” police control room officer Morgan Eriksson told the TT news agency.
The investigation was set to continue on Wednesday morning.
The southern Swedish city of Malmö has seen a spate of car burnings over the summer, while car fires have also been reported in other cities across Sweden, including Stockholm, Gothenburg and Norrköping.