"Tournament director Mike Stewart has reviewed the incident and feels there has been a breach of the tour code of conduct and consequently Tiger Woods will be fined," the European Tour said in a statement on Monday.
Officials will now write to the 35-year-old American's management team but are unlikely to publicly disclose the amount of the fine.
"You look at his work ethics and he is a credit to the game and an inspiration to all of those who are trying to become professional golfers but there are some parts of him that are just arrogant and petulant," said Briton Murray.
"Somebody now has to come behind him and maybe putt over his spit (on the 12th green). It does not get much lower than that."
"Could you imagine Jack Nicklaus looking down at a four or five-foot putt and then turning to the side and (spitting)? It would never happen," said former tour professional Lee.
"It's a lack of class, appalling. It won't be his legacy, his legacy will be that he has won 14 majors and...if he is not the best golfer who ever lived, he is very close to it.
"But he should also be mindful of where he is in world golf and what youngsters think of him because whether he likes it or not, he's a role model."
Lee said he could never imagine past golfing greats spitting on the course in the manner of Woods.
"I keep looking at that vision of him squatting down at the 12th green...could I ever see Nicklaus, Tom Watson, Bobby Jones, Ben Hogan, any of those legends doing something like that? The answer is 'no'," said the Briton.
"He needs to have a bit more class about him and think about what he is doing."
(Editing by John Mehaffey)