Designated hitter Manny Ramirez also left the game after getting hit by a pitch on the left wrist in the eighth inning -- the second time he was hit in the game.
Garcia gave up a pair of runs on a home run to the Tigers' Johnny Damon in the first inning. Garcia lasted just 33 pitches, giving up three hits.
"When a pitcher like Freddy says he has to come out of the game, you know something is really wrong," manager Ozzie Guillen said. "I don't know if he'll be ready for Sunday, and I'm not sure what our Plan B will be, but we have options if we need them."
Lucas Harrell came on in relief to start the bottom of the third and allowed four runs that inning.
In his last outing Wednesday at Cleveland, Garcia went four innings (60 pitches).
Ramirez was unable to get out of the way of a fastball from the Tigers' Robbie Weinhardt. He winced in pain behind home plate and after a short visit from trainer Herm Schneider and Guillen, he walked straight to the White Sox's dugout. He was replaced on the base paths by Alejandro De Aza.
Ramirez was also hit on the left elbow by Justin Verlander in the sixth inning.
"I think Manny is going to be OK, but we'll have to see tomorrow," Guillen said. "The ball hit mostly meat, so he should be fine."
In other White Sox injury news, Paul Konerko (back) and Gordon Beckham (hand) didn't start Tuesday.
Shortly before Ramirez was hit and had to leave the game, Tigers first baseman Miguel Cabrera left with left shoulder biceps tendinitis.
Doug Padilla covers the White Sox for ESPNChicago.com and ESPN 1000. Information from The Associated Press contributed to this story.
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