Williams, who was sacked by the ex-world number one during the summer after 13 years together and is now caddy for Australian Adam Scott, disparaged Woods at a caddies awards dinner in Shanghai on Friday night.
He had told the audience that the aim of his celebration when Scott won a world championship in August was "to shove it right up that black a*******".
Williams subsequently issued an apology on his website while admitting the comments "could be construed as racist".
The incident has attracted international criticism but the 47-year-old looks to have escaped any official sanction from the PGA and European tours.
A joint statement from European Tour chief George O'Grady and PGA Tour commissioner Tim Finchem on behalf of the International Federation of PGA Tours, released following the end of the WGC-HSBC Champions tournament in Shanghai on Sunday, read: "The International Federation of PGA Tours feels strongly there is no place for any form of racism in ours or any other sport.
"We consider the remarks of Steve Williams, as reported, entirely unacceptable in whatever context.
"We are aware that he has apologised fully and we trust we will not hear such remarks again. Based on this, we consider the matter closed, and we will have no further comment."