Watson, who had been scheduled to tee off in Thursday's opening round in a high-profile grouping with three-times winner Phil Mickelson and defending champion Brandt Snedeker, has been replaced by US PGA Tour veteran Billy Mayfair.
"Pulling out of tourney this morning, don't have energy for golf. Feel the same as Maui. Got to say thanks to my peeps for the prayers!," Watson tweeted earlier on Thursday.
"Wife and I are sick, hope little man doesn't get it. Time to rest and be ready to play next week."
Left-hander Watson endured a stomach complaint in the US PGA Tour's season-opening Hyundai Tournament of Champions in Maui where he tied for fourth and has not competed since then.
A four-times winner on the US PGA Tour, he is one of the biggest drawcards in the game with his prodigious length off the tee and his creative shot-making.
Watson is also a former champion at the Farmers Insurance Open, having triumphed by one shot in 2011 after holding off late charges by Mickelson and Venezuela's Jhonattan Vegas.