World number one Woods was photographed accepting the hand of Garcia as the pair practiced at Merion ahead of this week's US Open.
A rift developed between the two last month when Garcia made comments which could have been construed as racist about the American.
When asked if he would ever have Woods over for dinner, Garcia said he would serve him "fried chicken", echoing similar comments made by Fuzzy Zoeller in 1997.
Woods branded the comment as "hurtful" and "clearly inappropriate", with Garcia apologising and insisting it did not have racial intentions.
The feud between the two started at the Players Championship last month, with Garcia unhappy about Woods' conduct on the course.
The Spaniard made his fried chicken comment when on stage at the European Tour's annual awards ceremony.
With Garcia in Philadelphia for this week's tournament there have been concerns that he would be revoked by the American fans, with fellow European Justin Rose telling ESPN: "I fear there will be a backlash."
Garcia appears to have tried to stifle any dissent, though, having approached Woods and offered him his hand. Woods refused to comment when asked by reporters, although both are set to face the media on Tuesday.