Frazier immediately left after the play in the fourth inning Wednesday at Texas.
Frazier was going after Prince Fielder's popup when he reached out while getting close to the short brick wall separating the field from the first row of seats. The ball appeared to hit Frazier's glove before popping out, and he fell face-first into the seating area while fans scattered.
"My momentum took me into the stands, and my head went right into the arm rest," Frazier said. "Basically, I felt my tongue went through my bottom lip. Ice it up a lot, and I'll be good to go for Friday."
None of the fans appeared to be injured. Frazier got up and covered his face with his glove before going straight into the White Sox dugout nearby.
The team said Frazier is day-to-day. He is in his first season in Chicago, which acquired him in a trade last winter after he played his first five major league seasons with the Cincinnati Reds
Frazier had led off the top of the fourth with his third homer in the three-game series.
Carlos Sanchez took over at third base. A few batters after he entered the game, there was a foul pop that landed a few rows deep into the seats. Sanchez drifted over and stopped at the wall.
The AL Central-leading White Sox dropped their second straight game, 6-5.
Information from The Associated Press was used in this report.
Frazier leaves game after diving into stands
White Sox 3B Todd Frazier exits the game in the bottom of the fourth inning against the Rangers after diving head first into the crowd and appearing to injure his face in the process.