Palmer, a seven-time major champion, said that while he did not know the specific nature of the surgery he felt optimistic about Woods's golfing future.
"Tiger is in such good physical condition, and has been through his life, that they must know they're doing the right thing by doing the surgery," Palmer, 84, said on a conference call promoting a documentary on his life that will be aired on the Golf Channel.
"He is also determined enough in his personality and his well-being that he will overcome any of the problems that might be created physically.
"Do I think he'll be a potential player to be worried about? Yes ... and I think the potential for him to win future major championships is still very real."
Woods withdrew from last month's Arnold Palmer Invitational, an event he's won eight times, because of his back pain and has been stuck on 14 majors since winning the 2008 U.S. Open.
Palmer is credited with helping to popularize the sport as his daring style of play and charisma spawned huge throngs of fans that became known as "Arnie's Army" just as the growing medium of television began its love affair with sports.
After his serious days as a competitor, Palmer, a winner of 62 PGA Tour titles during an illustrious career, helped create a channel dedicated exclusively to the game he loved.
"Mr. Palmer was one of the two founders of Golf Channel nearly 20 years ago, and it's a very special project for that reason because he is so near and dear to all of our hearts," said Golf Channel president Mike McCarley.
"Also because (of) his influence on the game and the impact that he's made on sports and popular culture."
Palmer, whose last major championship came at the 1964 Masters, said he was watched bits and pieces of the documentary.
"It brought me back to my world of so many years ago," said Palmer. "I really can't even think about it. It made me think and get pretty emotional."
With the Masters rolling into action next week at Augusta National, Palmer spoke fondly of the club's co-founders, Bobby Jones and Cliff Roberts, and of his unlikely golf buddy, former U.S. President Dwight David Eisenhower.
"Seeing this replay of all my life to a degree, it's brought back people like, well, President Eisenhower," said Palmer.
"Who in the hell would have ever thought that a greenkeeper's son from Latrobe, Pennsylvania ... would ever play golf with the President of the United States or sit in my living room and have a glass of wine with the President of the United States."
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