Woods announced his withdrawal from the event, which his foundation runs and uses as a charity benefit event, on his website on Wednesday.
"I have been advised to take a few weeks off, rest and undergo treatment," Woods said. "I'll be ready to go for the British Open and I'm looking forward to playing at Muirfield."
The US PGA tournament, one of the last major US tuneups for the British Opens, runs June 27-30 at Congressional Country Club in suburban Washington.
Woods, whose 14 major titles are four shy of the record 18 won by Jack Nicklaus, injured the elbow last month on his way to victory at the Players Championship, although that was not common knowledge until last week's US Open.
Woods aggravated the injury last week blasting out of the dense rough at Merion and played through pain on the way to a share of 32nd place at 13-over par 293 total, his worst 72-hole professional US Open score relative to par.
"I was examined after I returned home from the US Open and the doctors determined I have a left elbow strain," Woods said.
The 37-year-old American has won four times this year, giving him 78 career titles, only four shy of matching the all-time PGA triumphs record set by the late Sam Snead.
Woods expressed regrets to sponsors and fans for not playing but said he will attend the tournament.
"It's especially difficult not defending at my own tournament," he said. "It's going to be a great event and I look forward to being there to provide my support."