The Spaniard apologised the next day but his remarks harked back to a controversy in the late 1990s involving former PGA golfer Fuzzy Zoeller who referred to Woods serving "fried chicken'' at the Masters champions dinner.
Garcia's comments followed a clash with Woods in the third round of the Players Championship earlier this month when the two were grouped together and Garcia said he was distracted by crowd noise after the American pulled a club out of his bag.
Garcia tried to explain his position last week in England.
"I mean, you can't like everybody,'' he said.
"He doesn't need me in his life and I don't need him in mine. Let's move on and keep doing what we are doing.''
Woods tweeted in response to the "fried chicken'' comment: "The comment that was made wasn't silly. It was wrong, hurtful and clearly inappropriate ... it's long past time to move on and talk about golf.''
Jack Nicklaus, host of the Memorial Tournament, weighed in on the topic on Wednesday, calling the controversy ``stupid''.
"Nobody needs that. And I think both finally said it's enough. Let's move on,'' Nicklaus said.
Dealing with racial stereotypes is nothing new to Woods.
"Well I live with it,'' he said on Wednesday.
"It's happened my entire career. It exists all around the world, not just in the sport of golf. It exists everywhere. I know a lot of people are trying to make a difference and trying to make it more fair for all of us.''
Woods, who has already won four times this year, returns to defend his title at Muirfield Village which he will use as a tune-up for the US Open.
The 14-time major winner is off to one of his best starts to a season in his career.
Defending the Memorial title, however, will not be easy as 17 of the world's top 25 players are in the field this week.
-AAP