Authorities are yet to ascertain what caused the fire, but the 61-year-old and his family have been left "shaken and shocked" by the incident.
Emergency operators were called to the home of outgoing Celtic chief executive
in the early hours of Wednesday morning, prompting a police search in Glasgow.
Around 1 am (BST), fire and Rescue departments were alerted to the news of a vehicle on fire, and eight fire trucks were dispatched to put out the blaze.
Lawwell's family was physically unharmed in the incident, but they are shocked to see their house burn with an explosion.
"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.
"Clearly, Peter's family are extremely shaken and shocked by these terrible events, but thankfully all are safe. We understand that Police Scotland are currently undertaking a criminal investigation.
"Peter and his family will of course receive the full support and care of everyone at the club."
Meanwhile, Scotland Police issued a warning of their own, which read:
"Around 1 am on Wednesday, 19 May, officers were called to a report of vehicles on fire outside a house on Peel Road, Thorntonhall.
"No one was injured and officers are currently working with the Scottish Fire and Rescue Service to establish the cause of the fire.
Fire and Rescue added:
"Operations Control mobilised eight appliances to the scene to extinguish the fire, which was affecting a number of cars as well as the detached two-storey property. There are no reported casualties."
Lawwell is due to step down as chief executive at Celtic Park at the end of the season, to be succeeded by Scottish Rugby's chief operating officer Dominic McKay.
The 61-year-old's run in Scottish football has been somewhat favorable, but a disastrous 2020-21 season that saw Rangers dethrone the Hoops asScottish Premiership
champions, raised concerns about the club's management.