Initial tee times were pushed back three hours before play eventually started at Torrey Pines but the action was halted just five minutes later as visibility swiftly deteriorated.
With the sun briefly breaking through, officials prepared for a re-start at 12:20 pm local but those plans were swiftly abandoned as another blanket of fog rolled across the coastal venue.
"We basically lost the whole day today, so we'll be back here in position at 7:00 (1500 GMT) in the morning," Mark Russell, the US Tour's vice president of rules and competition, said.
"We're going to play golf all day until dark and then when it gets dark, we'll suspend play. We'll come back Monday morning and finish the championship if the weather cooperates. That is the plan.
"Usually with over 78 players (left after the second round) we make a cut after the third round, but we're not going to make a cut. We're not going to re-pair. We'd lose too much time."
Asked what time he expected the tournament to finish on Monday if the weather cooperated over the next two days, Russell replied: "Ballpark, we're going to have anywhere from 12 to nine holes Monday, something like that.
"We will play 72 holes. If we get half the field in (finished) in the final round, the round must stand."
Former world number one Woods leads the tournament by two shots, having taken control with a superb seven-under-par 65 in rain-sodden conditions during Friday's second round.
A six-times champion in the US Tour event at Torrey Pines, Woods finished at 11-under 133 with little-known American Billy Horschel alone in second after carding a 69.
"I have been out here long enough to know that this is part of the game," Woods said of Saturday's near-washout because of the fog. "I'll be ready to go tomorrow."
Woods has gone on to win 34 times out of 44 when holding at least a share of the 36-hole lead on the US Tour and he heads a relatively weak leaderboard going into the final two rounds.
Of his 14 closest pursuers, only Australian John Senden and American Nick Watney have previously won on the US Tour.
Horschel, who has been grouped with Woods and fellow American Casey Wittenberg for the final two rounds, was stunned that the fog stayed around for most of the day.
"I knew it was going to get foggy out here, but I didn't expect it to be this bad," he said. "Up at Pebble (Beach), I've been there when it's been foggy, and had several hours to wait, but nothing where the whole day has been washed out."
Asked what he had done to pass the time, Horschel replied: "Eat a couple of times, sit down, relax, chit chat, come out here and putt, chit chat with everyone else. Just try to stay loose. It's all I've done, really."
Saturday's fog delay was the first at the Farmers Insurance Open since 2005 when play was suspended on the second and third scheduled days of the event.