Emergency services were called to Cllr Graeme Campbell’s house in Fortrose Gardens, Strathaven at about 12.20am on Saturday.
Two cars were set on fire and the blaze spread to the house, causing significant damage.
Scottish Fire and Rescue Service extinguished the blaze and there were no injuries.
The Scottish Conservatives said it was the third time Mr Campbell’s home has been targeted and police are treating the blaze as suspicious.
The party’s shadow community safety minister Russell Findlay said: “Councillor Campbell and his wife could have been killed in this disgusting and cowardly attack.
“They are understandably devastated. These are decent, law-abiding people and it is the third time their home has been targeted.
“I will be seeking assurances from the Scottish Government, Crown Office and Police Scotland that this attack is investigated to the fullest possible extent.
“There must be zero tolerance towards any attack of this nature. Organised criminals prey on communities across Scotland. Fire is indiscriminate and even where the intent is to intimidate, it can kill.”
Mr Findlay earlier wrote on Twitter that “it took 40+ min for police to attend” the incident.
A Police Scotland spokeswoman said: “We can confirm police officers were dealing with two serious and ongoing incidents when the call was received.
“Police were advised those involved were safe and officers attended as quickly as possible. We are engaging and supporting those affected by this incident and are currently appealing for any information which could assist the investigation.”
Officers said a man in dark clothing was seen in the area around the time the fire started.
Detective Chief Inspector Martin McGhee said: “I am appealing to anyone who may have been in the area around the time of the incident. Did you notice anything suspicious or see anyone acting oddly?
“I would ask any motorists or taxi-drivers with dash cam devices to check their footage as the device may have captured images which could assist our investigation. Any small piece of information could assist us in identifying who is responsible for this attack.”
Anyone with information can contact police by phoning 101.
Additional reporting by PA.