While the 85-year-old Palmer has vowed to overcome a shoulder injury to fulfil his ceremonial tee-off role at the Masters, Woods is still trying to get his game in shape.
The former world No. 1 has competed only twice this year, missing the cut at the Phoenix Open in early February before withdrawing in the first round of the Farmers Insurance Open due to his ongoing back problems.
"Tiger called me personally to let me know that he wouldn't be playing here at Bay Hill," Palmer said on his PGA Tour event's website.
"He said that his game is not quite ready yet and that he was disappointed that he won't be able to play in the tournament, which has always meant a lot to him. I'm sorry that he won't be playing. We'll certainly miss him, but I understand and appreciated that he called me."
Woods has won the Arnold Palmer Invitational a record eight times, the last of which came in 2013.
However, he has not added to his total of 14 major wins since 2008, but hopes to be in contention at Augusta from April 9-12.
"I've put in a lot of time and work on my game and I'm making strides, but like I've said, I won't return to the PGA Tour until my game is tournament ready and I can compete at the highest level," the 39-year-old said on his website.
"I hope to be ready for the Masters, and I will continue to work hard preparing for Augusta."
Palmer first hosted the Bay Hill tournament in 1979 and it took his name from 2007. It raises money for two Florida hospitals named for the seven-time major winner and his late wife Winnie.
"I am so proud of what has been accomplished at the hospitals over the past 25 years. It is always a privilege to know that we are making a difference in the lives of families throughout the community," said Palmer after his medical center was named one of the best for children in the U.S. for 2014-15.
He hurt his shoulder in December after tripping on carpet when he was about to make a speech at a PGA Tour father/son event.
World No. 1 Rory McIlroy will make his first appearance at Palmer's March 19-22 tournament, which features a restricted field, while top-five players Bubba Watson, Henrik Stenson, Adam Scott and Jason Day will also take part.