Brian Moore and his family escaped injury after their family car was set alight in Lislane Drive, Creggan at around 4 am on Saturday.
Police have described the act as “reckless” and are treating it as arson with intent to endanger life.
Sinn Féin Foyle MLA Raymond McCartney condemned the attack on his colleague.
“Thankfully no one was hurt, although it could have been much worse as the family were in the house at the time,” he said.
“The criminal elements responsible for this attack have nothing to offer but continually bring a bad name to Creggan. They should get off the backs of the community.”
Police are appealing for anyone who witnessed anything suspicious around the time of the fire to contact them.
Detective Sergeant Marshall said: “We received a report around 4:10am that a vehicle parked close to a property had been set on fire.
“Extensive damage was caused to the vehicle while damage was also caused to guttering and fascia boards of the house.
“This was a reckless attack and those responsible for this crime showed complete disregard for the two adult occupants of the house and other residents in the area.
“We are fortunate no-one was injured.
“This is being treated this as arson with the intent to endanger life, and I would appeal to anyone who was in the area around this time and saw any suspicious activity, or anyone who has information about this crime to contact detectives at Strand Road on 101 quoting the reference number 425 29/06/19.”
Alternatively information can be provided to the independent charity Crimestoppers on 0800 555 111, which is 100% anonymous and gives the power to people to speak up and stop crime.