Chicago eventually fell to the Mariners, 5-4.
"We're going to check after I finish talking to you guys. He got hit in the elbow. He bruised it up so in the end we took him out because he was feeling a little difficulty moving his arm. We'll check on him but he should be fine," White Sox manager Rick Renteria said after the game.
Garcia was 0-for-1 with a walk at the time he was hit. He's hitting .298 this season.
Garcia was batting against Mariners starter Sam Gaviglio with two out and a runner on second base in the top of the fifth when Gaviglio's 88.2 mph two-seam fastball struck Garcia on the arm.
Garcia was replaced in center field by Willy Garcia in the bottom of the inning.
Doug Miller is a reporter for MLB.com. Follow him on Twitter @DougMillerMLB. This story was not subject to the approval of Major League Baseball or its clubs.