A large crowd of youths in the Galliagh area of the city threw stones at fire crews attending the scene on Wednesday evening.
The police were also in the area after reports of the same car being driven dangerously on the Fairview Road.
The Northern Ireland Fire and Rescue Service (NIFRS) have appealed for an end to attacks on crew members.
"Thankfully, there were no injuries to firefighters and whilst no damage was caused to the appliance, we would appeal to the local community not to threaten or attack firefighters responding to emergency calls," said a NIFRS spokesperson.
"These attacks are not only socially unacceptable but they can be detrimental to the whole community if firefighters or appliances are hindered in any way when responding to emergency calls.
"Dealing with deliberate fires ties up vital resources from other more serious incidents and potentially puts people and property at risk."
The spokesperson added that firefighters returned to the scene on Wednesday night and "dealt with the deliberate car fire".
Sinn FÃ©in councillor Elisha McCallion described those behind the attack as "thugs".
"The activities of these anti-community elements, while putting the lives of residents at risk, also disrupted the operation of the Galliagh Co-op which had to close when these thugs set fire to the car in which they were death-driving around the area," she said.
"The residents of the greater Galliagh area are fed up with the antics of this minority element and demand that they cease this activity before there is a fatality or serious injury."
The PSNI said officers had liaised with local community representatives and no further incidents were reported.
Firefighters have come under attack in Londonderry as they responded to reports of a car on fire.