The company he founded in the 1950s, Arnold Clark Automobiles, announced he had died peacefully at home today.
It released a statement saying it was saddened to announce the passing of its founder and chairman.
"Sir Arnold was a truly inspirational business leader and influential public figure," the company said.
"His unsurpassed work ethic and strong family values led him to build a market-leading automotive retailer that continues to go from strength to strength.
"Sir Arnold's entrepreneurial ideals continue to be at the heart of the business.
"His personal philosophies will continue to inspire everybody who works in the business, and will be the cornerstone of its future growth and continuing success.
"Our thoughts are with his family at this difficult time."
And a family statement reads: "Sir Arnold Clark passed away peacefully this morning, 10 April 2017, surrounded by his family. He was a beloved husband, father, grandfather and a great friend and employer to many.
"He was an inspiration and the family will continue to carry on his vision. He will be greatly missed.
"We wish to thank all those who have sent messages of condolence and appreciate your kind support.
"We ask for privacy at this difficult time to allow the family to grieve."
Sir Arnold was knighted in 2004. He founded the dealer group after leaving the RAF and opened his first dealership in 1954.