Woods has not played since withdrawing from last month's Dubai Desert Classic because of back spasms, part of a recurring injury that has plagued his career for the best part of three years and resulted in multiple surgeries.
Woods said there was "no timetable" for his return but told his website "treatments are continuing and going well."
The latest setback casts serious doubt on the 14-time major champion's appearance in the upcoming Masters, 20 years after he won his first major there as a 21-year-old.
"Unfortunately, due to ongoing rest and rehabilitation on my back, I won't be able to play in this year's Arnold Palmer Invitational," Woods, 41, said in the statement.
"I'm especially disappointed because I wanted to be at Bay Hill to help honor Arnold. This is one event I didn't want to skip. Arnold has meant so much to me and my family; I thought of him as a close friend.
"He will be greatly missed and can never truly be replaced."
Palmer, a golfing icon and seven-time major winner, died aged 87 in September last year shortly before the Ryder Cup.
Woods, an eight-time winner of the Arnold Palmer Invitational at Bay Hill in Florida, returned to golf in December following a 15-month lay-off from the game.
He missed the cut in his 2017 opener at Torrey Pines, and withdrew after a first-round 77 in Dubai. He also pulled out of a scheduled news conference at the Genesis Open at Riviera in aid of his foundation to rest his back.
Before the Dubai event, Woods told CNN he feared he would never play again after the "dark times" of injury.
The Arnold Palmer Invitational begins on March 16, just 20 days before the Masters.