As reported earlier on Wednesday, firefighters were called to the blaze on Peel Road in Thorntonhall, South Lanarkshire, at around 1am on Wednesday which forced Mr Lawwell and his family to flee their home.
Celtic FC said the family are “extremely shaken and shocked” by the blaze, which caused “significant damage”, but they are all safe.
Eight fire engines were sent to the scene to extinguish the blaze, but some crews were still at the scene at 7am with police road closures in place.
A joint investigation by Police Scotland and the Scottish Fire and Rescue Service has found three vehicles were deliberately set alight, which also resulted in extensive damage to the garage.
Detectives are treating the fire as deliberate after CCTV showed a man pouring an accelerant on the vehicles.
The male suspect is described as around 5ft 10in and of slim build.
He was wearing black joggers, a black hooded jumper with the hood up, black trainers and a face mask.
A silver or grey hatchback car was also seen near the house at the time of the fire.
Detective Inspector Susie Cairns said: “This was a completely reckless act which destroyed three cars and caused significant damage to the property’s garage.
“The consequences could have been so much worse but thankfully nobody was injured during this incident.
“I am appealing to anyone who was in the area at the time that saw a man or car matching this description or saw any unusual activity to please come forward.
“If you have personal CCTV or a dashcam, please check back and see if there is any footage that could assist our investigation.
“No matter how small or insignificant you think it may be, please get in touch.”
A Celtic spokesman said: “We can confirm that significant damage has been caused to Peter Lawwell’s house and vehicles there, following an explosion and fire early this morning, forcing the family to leave the property.”
Anyone with information is asked to contact police on 101, quoting reference number 0134 of May 19, or call Crimestoppers anonymously on 0800 555 111.