Officers received reports of a car on fire on Arondale Road in Plains around 9.05 pm on Monday.
The car, a black Ford Fiesta ST was extinguished by the Scottish Fire and Rescue Service and had substantial damage.
The fire is being treated as suspicious and Detective Constable Lyndsay McKinnon of Lanarkshire CID commented: “We are appealing for information from members of the public relating to this deliberate fire.
“Thankfully no one was injured as a result of this reckless act. But I would like to stress how dangerous wilful fireraising is and discourage anyone from setting a fire deliberately and know that officers will always investigate any report robustly and thoroughly.
“If you saw anything suspicious and have any information or were in the area and recording via dashcam, please check your footage for anything of relevance and contact police as soon as possible.”