Prior to the crash, Woods had not ruled out playing in next month's Masters - though he has not competed at a major since missing the cut at The Open in July 2024.
"I'm committed to taking the time needed to return in a healthier, stronger and more focused place, both personally and professionally," his statement added.
"I appreciate your understanding and support and ask for privacy for my family, loved ones and myself at this time."
Regardless of whether Woods was to play at the Masters, he was expected to be in attendance on the Sunday for the unveiling of The Patch - a revamped public golf course he has worked on with the Augusta National club
He was also expected to attend Rory McIlroy's champion's dinner on the Tuesday night.
"Augusta National Golf Club and the Masters Tournament fully support Tiger Woods as he focuses on his wellbeing," said Masters chairman Fred Ridley.
"Although Tiger will not be joining us in person next week, his presence will be felt here in Augusta."
The PGA Tour also issued its first comment on Woods following the golfer's statement.
"Tiger Woods is a legend of our sport whose impact extends far beyond his achievements on the course," it said.
"But above all else, Tiger is a person, and our focus is on his health and wellbeing. Tiger continues to have our full support as he takes this important step."
The golf body's chief executive, Brian Rolapp, added: "Tiger Woods is one of the most influential figures the sports world has ever known.
"Over the last year, I have come to deeply appreciate Tiger not only for his impact on the game, but for his friendship and the perspective he has shared with me as I joined the golf industry.
"My thoughts are with him and his family as he takes this step, for which he has my full respect and support."
Last week's accident was the latest in a string of incidents that have littered Woods' recent years.
His marriage ended - as did lucrative sponsorship deals - after he struck a fire hydrant, a tree and several hedges outside his home in a 2009 incident, sparking accusations of extra-marital affairs.
In 2017 he was sentenced to a year's probation after pleading guilty to reckless driving. That came after police officers found Woods slumped at the wheel of his car near his home. A toxicology report found he had several legal medications in his system and marijuana's active ingredient.
In 2021, Woods survived a serious accident which left him with extensive injuries. He has had multiple surgeries since, and played only a limited schedule.
Last week, he competed in the TGL indoor golf league - his first competitive golf for more than a year - following more back surgery and an Achilles tendon injury.
