Pierzynski sustained the injury while swinging during Chicago's 7-4 win against the Twins on Monday.
The injury doesn't affect Pierzynski defensively, but it bothers him at the plate.
"He won't play tomorrow, just to be safe," White Sox manager Robin Ventura said following Tuesday night's 11-4 win. "It's just one of those things you've got to monitor and make sure that it doesn't get worse. I would see him tomorrow and then having the off-day [on Thursday] and then being ready on Friday."
Pierzynski, 35, leads all American League catchers in RBIs (50) and slugging percentage (.507), while ranking second in batting average (.287), home runs (16) and runs scored (40).
Backup Tyler Flowers started Tuesday in place of Pierzynski.