The world number three, who has already missed two Majors this season, underwent an operation for a pinched nerve at the end of March.
"Unfortunately, I won't be there because I'm not yet physically able to play competitive golf," Woods said in a statement.
"Despite missing the first two majors, and several other important tournaments, I remain very optimistic about this year and my future."
He added: "I'd like to convey my regrets to the USGA leadership, the volunteers and the fans that I won't be at Pinehurst."
The North Carolina tournament, which takes place between June 12 and 15, will be the sixth Major that Woods has missed through injury.