At a caddies' awards party last week, Williams was given a light-hearted award for an interview he gave following the win of his new employer Adam Scott at the Bridgestone Invitational.
The Bridgestone was two weeks after Woods fired Williams.
Asked about the interview, Williams replied, "It was my aim to shove it up that black a***hole''.
Williams has denied he is a racist and said his comments were made in jest.
But the outburst has the golfing world questioning whether the clean-cut Scott, whose sponsors include Rolex and Titleist, will keep Williams as a caddie.
One source from one of the tours told AFP: "It's going to be difficult for Adam Scott if sponsors think he has a racist carrying his bag.''
But Scott played down Williams' outburst.
"I don't see it being an issue moving forward. I think from my side of things and my teams, the matter has been put to bed,'' he said after the final round of the HSBC Champions yesterday, ESPN reported.
PGA Tour commissioner Tim Finchem and European Tour chief executive George O'Grady issued a statement, saying they spoke for the International Federation of PGA Tours that it "feels strongly there is no place for any form of racism in ours or any other sport'', ESPN said.
"We consider the remarks of Steve Williams, as reported, entirely unacceptable in whatever context," the statement said.
"We are aware that he has apologised fully and we trust we will not hear remarks ever gain. Based on this, we consider the matter closed, and we will have no further comment."
Scott was shown a copy of the statement after signing his card and said he felt comfortable with it.
"I don't think anyone condones racism in sport or anything,'' he said.
Williams may come face to face with Woods in the next couple of weeks - with the Australian Open and Presidents Cup at Royal Melbourne.
