The car stood parked by Frölunda square when police received a call at around 11pm on Thursday evening.
“The fire was explosive and spread to three other cars,” said Christina Corneliusson at Frölunda police.
“The car has been taken in for technical inspection,” Corneliusson said.
The car is the third vehicle that has been set alight in the city recently. The other two attacks, in Hovås and Åskered, involved cars registered to Gothenburg restaurant owners.
The vehicle in Frölunda is registered to a woman but police would not confirm if she has a connection to the restaurant trade in the city.