The 43-year-old, eight-times victor of the tournament at Bay Hill in Orlando, announced on Twitter that he had been struggling with the problem for some time.
Day said he still aims to recover in time for next week's Players Championship at TPC Sawgrass.
The Arnold Palmer Invitational starts Thursday at Bay Hill Golf Course in Bay Hill, Fla.More news: India beats Australia by six wickets in opening ODI
Woods, ranked 12th in the world, played a full schedule a year ago for the first time since 2015, which came after the first of what would turn out to be four back procedures.
"I've been receiving treatment, but it hasn't improved enough to play".
Assuming Woods plays next week and comes out of it with no injuries, then he will likely add one (or maybe even two) more tournaments to his schedule before Augusta. His primary aim is to be fully healthy for the first weekend in April, for the Masters at Augusta National.
Woods said, "Its connection to Arnold makes it one of my favorite tournaments and I'm disappointed to miss it".
And think about this: If the PGA Tour schedule stayed the same as it was last season, when the Valspar Championship was in early March, Woods would be withdrawing from our tournament.