A car belonging to Sinn Fein Derry City and Strabane District councillor Kevin Campbell has been burned outside his home in the Creggan area of Derry.
Campbell, a former IRA prisoner, has previously served as Mayor of Derry.
Sinn Fein Foyle MP Elisha McCallion said her thoughts were with Cllr Campbell and his family.
"My thoughts are with my friends and colleague Kevin Campbell, his wife and their teenage daughter who where woke last night after thugs set fire to their car in the drive of their home.
"Kevin and his family are well respected Republicans and community activists in this city and we the people of Derry stand with you today.
"To the people who carried out this attack I ask you this, what did you think you were going to achieve?"
Police are appealing for witnesses following the attack in the Lislane Drive area of Derry.
"Shortly before 2.45am it was reported that a blue coloured Renault Modus parked in the area had been set on fire. Extensive damage was caused to the car as a result of the incident. Three people were seen running away from the scene," a PSNI spokesperson said.
"Police are working to establish a motive for the attack and are appealing for anyone who witnessed the incident or anyone with any information which may assist the investigation to contact officers in Strand Road Police Station on 101 quoting reference 249 08/04/18.
"Alternatively, information can also be provided to the independent charity Crimestoppers on 0800 555 111 which is 100% anonymous and gives people the power to speak up and stop crime."
Local community group the Creggan Neighbourhood Partnership condemned the attack.
"This action is utterly wrong and must be condemned," the spokesperson said.
"If there are any issues within the community they should be sorted out through community dialogue.
"This attack is not justified or justifiable in any way."