The meeting during practice for the U.S. Open was the first between the longtime adversaries since Garcia made a "fried chicken" reference directed at Woods last month at a European Tour awards dinner.
Garcia has since apologised and Woods told reporters it was time to move on.
Tensions between the two flared last month at the Players Championship, when Garcia suggested Woods showed poor sportsmanship by pulling a club from his bag as the Spaniard was about to hit a shot. Woods's move sparked cheers from the galleries and Garcia sliced his shot into the woods.
The two later exchanged verbal jabs through the media over the incident, revealing animosity simmering between them over the years.
Bad feelings escalated with Garcia's ill-advised attempt at humour when he was jokingly asked if he would be having dinner with Woods during the U.S. Open week. He replied: "We'll have him 'round every night. We will serve fried chicken."
Woods responded to the reference, viewed as a racial stereotype, on Twitter by saying Garcia's words were "wrong, hurtful and inappropriate."