Woods posted a statement on his website saying he told Palmer in person that he would not be able to defend the title he won at Bay Hill last year.
“I personally called Arnold today to tell him that, sadly, I won’t be able to play in his tournament this year,” Woods said.
“I would like to express my regrets to the Orlando fans, the volunteers, the tournament staff and the sponsors for having to miss the event.”
Woods has been plagued by back problems since last year but his condition worsened over the past month.
The 38-year-old American failed to finish the Honda Classic at Palm Beach Gardens earlier this month, quitting after 13 holes in his final round.
Then he tweaked his back again on the last day at the WGC-Cadillac Championship in Miami a week later, tumbling out of contention with a final-round 78 to finish tied for 25th.
Woods won the last of his 14 majors in 2008 and said that he was uncertain whether he would be able to play in the Masters, starting at Augusta National on April 10.
“Unfortunately, my back spasms and the pain haven’t subsided,” he said.
“It’s too early to know about the Masters, and I will continue to be evaluated and work closely with my doctors.”
Woods missed the 2008 British Open and PGA Championships because after knee surgery and also skipped the 2011 U.S. Open and British Opens because of a recurrence of his knee problems.
But the American has never missed the Masters since he made his debut at Augusta National as an amateur in 1995.
The Arnold Palmer Invitational, starting on Thursday, is one of Woods’s favourite events and attracts most of the world’s top players.
Woods has won the tournament eight times, including each of the past two years, and would have been chasing an unprecedented ninth title.
The only other player to have won the same PGA event eight times is Sam Snead, who won the Greater Greensboro Open eight titles between 1938 and 1965.
“I am certainly sorry that Tiger is not able to play,” Palmer said in a statement.
“Quite obviously, we will miss having him here this week. He called me to tell me that his back was still giving him a lot of trouble and he didn’t feel he should play.
“I told him I understood and wished him well.”
(Reporting by Julian Linden; Edited by Larry Fine)