"I need to focus my attention on being a better husband, father, and person," Woods said on his Web site.
Woods and his wife, Elin, have been married five years and have a 2-year-old daughter and a 10-month-old son.
The announcement came two weeks after Woods crashed his SUV into a tree outside his Florida home, setting in motion a stunning downfall for the world's No. 1 player who for 13 years rarely made news off the golf course. One woman who said she had a 31-month affair with Woods shared a voice mail that she said Woods left her two nights before his Nov. 27 accident.
"I am deeply aware of the disappointment and hurt that my infidelity has caused to so many people, most of all my wife and children," Woods said. "I want to say again to everyone that I am profoundly sorry and that I ask forgiveness. It may not be possible to repair the damage I've done, but I want to do my best to try."
Woods has not been seen in public since the accident.
He gave no indication when he might return in what could be a pivotal year as he pursues the record 18 major championships won by Jack Nicklaus. Woods, who did not win a major this year, has 14.
The Masters, where Woods has won four times, is April 8-11. The U.S. Open is at Pebble Beach, where Woods won by a record 15 strokes in 2000, and the British Open returns to St. Andrews, where he has won twice by a combined 13 shots.
It will be the second straight year that a PGA Tour season begins without its star player. A year ago, Woods was recovering from reconstructive knee surgery that kept him out a total of eight months.
This is different.
"We knew before he was coming back," said Steve Stricker, one of Woods' favorite players on tour. "Now, we're not sure when he's coming back. But this sounds good. I hope everything works out for him."
The PGA Tour supported the decision.
"His priorities are where they need to be, and we will continue to respect and honor his family's request for privacy," PGA Tour commissioner Tim Finchem said in a statement, the tour's first public comment since Woods mentioned his "personal failings" and "transgressions" in a Dec. 2 statement. "We look forward to Tiger's return to the PGA Tour when he determines the time is right for him."
Woods' agent, Mark Steinberg, told The Associated Press that it was the right decision for Woods and his family.
"The entirety of someone's life is more important than just a professional career," Steinberg said in an e-mail to the AP.
"What matters most is a young family that is trying to cope with difficult life issues in a secluded and caring way. Whenever Tiger may return to the game should be on the family's terms alone."
Craig Parry, who played a practice round with Woods in Australia last month, said Woods brought the problems on himself.
"What he did was totally wrong," Parry said at the Australian PGA Championship. "And he's got no one to blame except himself. You can look at other people, but he's the one who's got to look in the mirror."
Woods was out of action from July 2008 until the end of February this year, and television ratings dropped 50 percent. The tour is trying to renew a half-dozen title sponsors, and it is to begin negotiations on the next television contract later next year.
As for Woods' corporate endorsements, all have stood by him for now.
"Tiger has been part of Nike for more than a decade," Nike said in a statement Friday. "He is the best golfer in the world and one of the greatest athletes of his era. We look forward to his return to golf. He and his family have Nike's full support."
Meanwhile, Accenture no longer has an image of Woods on the home page of its Web site. Earlier this week, Woods standing amid cactus plants studying his next shot was among three rotating pictures on the home page.
Steinberg said it would be "premature and inappropriate" to talk about Woods' specific business relationships.
"Suffice it to say, we have had thoughtful conversations and his sponsors have been open to a solution-oriented dialogue," Steinberg said. "Of course, each sponsor has unique considerations and ultimately the decisions they make we would fully understand and accept."
Earlier this year, Woods became the world's first athlete to surpass $1 billion in career earnings, according to Forbes magazine. His sponsors include Nike, Gillette, AT&T, Gatorade and Tag Heuer.
Woods last played a tournament Nov. 15 when he won the Australian Masters for his 82nd victory around the world.
Stricker, who went undefeated as Woods' partner at the Presidents Cup, said his leave was the right decision.
"I think it's great that he's going to put his family first and work things out," Stricker said from Naples, Fla., where he is playing the Shark Shootout. "Golf will always be there. He wants to make sure his marriage is right and everything is good on the homefront. We'll sure miss him on tour until he gets things taken care of."
Woods also indicated he would step away from the work of the Tiger Woods Foundation, which has served some 10 million children.
"There are millions of young people who have truly changed their lives through the foundation's programs, and millions more still counting on us for help," Woods said in a separate statement through his foundation. "I am committed to them and to the foundation's excellent work, and I know my staff will continue these efforts during my absence."
Associated Press Writer Dennis Passa in Coolum, Australia, contributed to this report.