In the early hours of the Saturday morning, three men approached a car parked on a drive in South Carbrain Road, and set it alight.
No-one was injured in the incident but the car, a BMW, has been totally destroyed.
There is limited information on the three suspects, all were wearing dark coloured clothing and one was carrying a white plastic bag.
Following the incident they ran off in the direction of Broomlands Road.
Officers have been carrying out door-to-door enquiries and are checking CCTV footage from the surrounding area for any information which could assist in their enquiries.
Detective Constable Iain Smith said: “Despite this crime being committed in the early hours of Saturday morning, I would like to appeal to local people who may have seen or heard something. Perhaps you saw three men in the area earlier in the evening or did you see three men running off up Broomlands Road.
“If you have any information, please do contact us. I would also ask motorists who were in the area to check their dash cams as it could hold footage which could help us identify those responsible for deliberately setting this fire.”
Anyone with information is asked to call officers at Cumbernauld Police Station via 101, quoting incident number 0824 of 25 May 2019. Alternatively, please call Crimestoppers on 0800 555 111 where information can be provided anonymously.