Woods had targeted the event, which he was also set to host, to make his return after undergoing back surgery last year.
But Woods, 49, wrote in a statement on X on Monday: "I planned to tee it up this week, but I'm just not ready. I did my best to prepare, knowing it's what my Mom would have wanted, but I'm still processing her loss.
"Thanks to everyone who has reached out. I hope to be at Torrey later in the week and appreciate the continued kindness since my Mom's passing."
Woods announced his mother's death on February 4, posting on X: "It is with heartfelt sadness that I want to share that my dear mother, Kultida Woods, passed away early this morning."
Woods did not reveal the cause of death of his mother, who the previous week had attended her son's TGL match in Florida. The former world number one's father, Earl, died in 2006.
He underwent surgery in September to address the back spasms which severely limited his tournament play last year.
He and his 15-year-old son Charlie finished second in the PNC Championship in December, and the 15-time major winner has since played twice for Jupiter Links in the TGL.
Woods has 82 PGA Tour wins to his name, eight of them at Torrey Pines, where he has claimed seven Farmers Insurance Open titles and the 2008 US Open.
The Genesis Invitational is being staged at the San Diego course between February 13-16 after being moved from the Riviera Country Club because of the impact of the wildfires in Los Angeles.
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