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 deteriorated.
With the sun briefly breaking through, officials prepared for a re-start at 12:20 p.m. local (2020 GMT) but those plans were swiftly abandoned as another blanket of fog rolled across the coastal venue.
"There is nothing we can do about it," Mark Russell, the PGA Tour's vice president of rules and competition, told reporters. "If Mother Nature doesn't want you to play you're not going to play.
"Hopefully, it gets better and we can play some golf. If not, we'll see what happens."
Though there was no prospect of the third round being completed on Saturday, Russell was hopeful the tournament would not spill over into a rare Monday finish.
"We need to play all the golf we can (today)," he said. "We need to get teed off in the next hour and half to have a chance (to finish Sunday)."
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 PGA Tour event at Torrey Pines, Woods finished at 11-under 133 with little-known American Billy Horschel alone in second after carding a 69.
Six players, including American Jimmy Walker (69) and double heart-transplant recipient Erik Compton (65), were bunched at eight under.
Woods has gone on to win 34 times out of 44 when holding at least a share of the 36-hole lead on the PGA 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 PGA Tour.