O'Grady apologized on Thursday: "I deeply regret using an inappropriate word in a live interview for Sky Sports, for which I unreservedly apologise."
The controversy began when the 33-year-old Spanish golfer addressed his ongoing problems with Woods at an awards dinner on Tuesday.
"We will have him round every night," Garcia said when someone asked whether he'd be inviting his American competitor over for dinner. "We will serve fried chicken."
Woods called the comment "wrong, hurtful and clearly inappropriate," while Garcia issued this statement:
I apologize for any offence that may have been caused by my comment on stage during The European Tour Players' Awards dinner. I answered a question that was clearly made towards me as a joke with a silly remark, but in no way was the comment meant in a racist manner.
Garcia also said he hoped to speak with Woods "face-to-face."
"If I manage to speak with Tiger, it will be perfect. If not, I will definitely see him at the US Open and we can talk face to face."