Police believe a gas cylinder had been placed in the vehicle and that a petrol bomb was also thrown at the house in the Sevenoaks area of the city.
A number of residents who were moved from their homes have been allowed to return.
PSNI Det Sgt Brian Reid said the man was injured while attempting to extinguish the fire in the car.
The man was taken to Altnagelvin Hospital for treatment to his injuries which are not believed to be life-threatening.
Police are working to establish a motive for the attack which was reported shortly after 3.30 am on Sunday.
Det Sgt Reid appealed for anyone with information to come forward.
“It is bad for people to get a knock from police in the morning to move out,” he said.
He said around 15 people were temporarily housed in the Foyle Arena.
“Two controlled explosions were carried out by ATO,” he said.
“This is a very quiet area and for a lot of people they haven’t seen anything like this.”
Sinn Féin councillor Christopher Jackson said the incident “must be very upsetting for anyone caught up in this”.
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