"I would like to thank Genesis for their support, and I know we will have an outstanding week."
The 41-year-old's future playing schedule will be determined at a later date, after his back is reassessed.
The Masters, the first major of the year, gets under way on April 6.
Woods posted the link to his statement on his Twitter account today, indicating he still planned to attend next week's tournament in Los Angeles.
"Really looking forward to seeing everyone @genesisopen open next week, unfortunately I won't be able to play," he wrote.
In his first 322 starts as a professional, Woods withdrew from just five events. In his last 19 starts, he has withdrawn four times.
The former world No.1 did not look 100% fit at various points during his opening round in Dubai and admitted earlier this week that he fears he will "never feel great" again, because of the number of injuries he has suffered during his career.