Garcia, who has been involved in a public row with Woods since the Players Championships at Sawgrass this month, was on stage with the rest of the victorious Ryder Cup team, including captain Jose Maria Olazabal.
During a question and answer session hosted by the Golf Channel's Steve Sands, the Spaniard was asked if he would have the world number one around for dinner one night during the upcoming US Open.
"We will have him round every night," Garcia said. "We will serve fried chicken."
Garcia later issued a statement through the European Tour, saying: "I apologise 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's remark was similar to one made by Fuzzy Zoeller to Woods in 1997. After Woods won the Masters which entitled him to choose the champions' dinner menu for the following year, Zoeller said: "You pat him on the back and say congratulations and enjoy it and tell him not to serve fried chicken next year. Got it? Or collard greens or whatever the hell they serve." Zoeller later apologised and said he had been misconstrued.
Just hours earlier, Garcia told reporters ahead of the BMW PGA Championship at Wentworth that there was no end in sight to his spat with Woods, which resurfaced after the pair had played together in the third round at Sawgrass.
Garcia felt he had been disturbed on his approach to the second hole when spectators cheered Woods for taking a fairway wood out of his bag, indicating he would try to reach the green from his position in the trees.
"He's not my favourite guy to play with," the Spaniard said. "He's not the nicest guy on Tour. We don't like each other. It doesn't take a rocket engineer to figure that out. He is who he is. I am who I am. It's best we're not playing together again."
Asked on Monday if he would call Garcia to clear the air, Woods simply said 'No'.
And Garcia said on Tuesday: "Obviously you can't like everybody. I think there's people that you connect with and there's people that you don't. It's pretty much as simple as that.
"He doesn't need me in his life, I don't need him in mine, let's move on and keep doing what we're doing.
"It's never really been a true connection like I would have with maybe Luke (Donald) or Lee (Westwood) or Adam Scott or some of the other guys that I get along with well.
"It's fine. It doesn't mean that I cannot play with him. It's just another player, obviously a good player.
"It's just when I'm playing with someone I enjoy, there's a bit more talking going round and when you're playing with someone that you don't fancy as much you're just a little bit quiet."
Garcia could now find himself in hot water with the European Tour, whose code of behaviour states that: "On becoming a Member each person voluntarily submits himself to standards of behaviour and ethical conduct beyond those required of ordinary golfers and members of the public.
"The European Tour has been the hallmark of honesty, fair dealings, courtesy, and sportsmanship and each Member is bound to honour and uphold that tradition at all times whether on or off the golf course."
The Tour handbook lists examples of potential minor or serious breaches of the code, including for 'injurious conduct' which is described as: "Actions or comments that may harm or discredit officials, fellow Members, sponsors, promoters, volunteers, third party contractors or the PGA European Tour and that does cause or is deemed likely to cause significant negative media or long term damage to any of the aforementioned persons."
Possible sanctions include a reprimand, censure, fine, suspension of membership or even expulsion from the European Tour.
Asked for his reaction to Garcia's comment on Twitter, Graeme McDowell wrote: "private/humor filled environment but he shouldn't have said it #slip," while Lee Westwood felt Woods would not be "particularly bothered" by it.
"It's an awkward situation where they obviously just don't get on," Westwood added. "It's in the public and you guys (the media) will stoke it up and you don't need to.
"I get on with both of them but I have no interest of getting in the middle of that relationship. It's nothing to do with me."