Garcia, an All-Star last season who hit .330 with 18 home runs and 80 RBIs, missed two months earlier this season with a more serious strain to the same hamstring muscle. White Sox general manager Rick Hahn said Garcia's new injury is "in a different location and considered more mild."
Hahn hopes Garcia will return after the All-Star break.
The 27-year-old outfielder is batting .282 with nine homers and 17 RBIs in 35 games this season. Since returning on June 22 from his first stint on the DL, Garcia was Chicago's hottest hitter with a .333 average, eight homers and 13 RBIs before leaving Sunday's game at Houston.
The White Sox added outfielder Ryan LaMarre, claimed off waivers from Minnesota, to their roster to take Garcia's place.