The infraction occurred on the par-four first at Conway Farms Golf Club where Woods struck his second shot over the back of the green under trees, then tried to remove a twig from his ball before playing his third.
Though Woods felt his ball had only oscillated before he ran up a double-bogey six there, video footage later showed that it had slightly shifted its position and his score was amended to a quadruple bogey eight.
The rules violation came to light as Woods was playing either his third or fourth hole of the day and the American world number one went on to card a one-over-par 72, ending the round seven strokes off the tournament lead.
Slugger White, the US Tour's vice president of rules and competition, advised Woods not to sign his card until he had viewed the video footage himself.
"I told him not to turn it in until I talked to him, and he looked at it, and clearly felt like the ball just oscillated," White said. "It's pretty clear that the ball did move."
Asked how Woods had initially reacted when told of his two-stroke penalty, White replied: "He was a little disbelieving. How's that?"
A disgruntled Woods, who posted a four-under total of 138 after 36 holes in the third of the US Tour's four FedExCup play-off events, swiftly left the scoring area, then marched past reporters before heading off to the locker room.
"Tiger evidently hit it over the green and was moving some loose impediments," White said of the infringement at the first.
"He had a pretty large loose impediment behind his ball, which he moved, was no problem at all.
"And there was a little stick of some sort kind of next to his ball, and when he rolled that, the ball in fact moved. He knew there was movement there, but was very adamant that it oscillated, it stayed there.
"But this video was at the site, and the ball did, in fact, move. So in that situation, had he put the ball back it would have been a one-stroke penalty. He didn't, so he gets a two-stroke penalty."
The infraction, filmed by a videographer working for PGA Tour Entertainment, was spotted by an editor, who immediately alerted Andy Pazder, the US Tour's executive vice president and chief of operations.
Padzer then contacted White, who said he was notified "maybe when Tiger was walking down (hole) three, maybe four".
It is the third time this year that Woods has been given a two-shot penalty for a rules violation.
His first infraction came in his opening event of the season, at the European Tour's Abu Dhabi Championship, where he missed the cut after taking a free drop from an imbedded lie in a sandy area under a desert bush.
The regulations, however, only allow for a free drop in such circumstances if the ball has finished anywhere but in sand and Woods was therefore handed his penalty at the end of the round.
He also fell foul of rules officials at the Masters after taking an illegal drop during the second round when his wedge approach at the 15th struck the flagstick before ricocheting backwards off the green and down the slope into Rae's Creek.